There is always a random nature to Week 17 in the N.F.L., and this year was no different. New England lost in shocking fashion to Miami, Tennessee and Philadelphia completed their circuitous journeys to the postseason and Baltimore’s backups beat Pittsburgh. But when put to the test, San Francisco, Green Bay and Kansas City all came through with big wins, joining the Ravens as the four playoff teams with first-round byes.

Here’s what we learned:

• The play clock is important. It looked like a Hollywood ending in Seattle. Marshawn Lynch, in his first week back from retirement, ran onto the field in the waning moments of a crucial game against the 49ers hoping to punch the ball in for game-winning touchdown from the 1-yard line. Some confusion on the field, and Seattle having used its last timeout, combined to run the play clock down to zero, resulting in a shocking delay-of-game penalty that backed the Seahawks up to San Francisco’s 6-yard line.

  After a pair of incompletions — one of which appeared to be the result of a missed pass interference call — led to a 4th-and-goal, Russell Wilson connected with tight end Jacob Hollister, who was crushed to the turf by linebacker Dre Greenlaw at the goal line in a play that was eerily reminiscent of the Julio Jones catch that beat San Francisco in Week 15. Both sides immediately believed they had won the game, but replays showed Hollister was stopped just fractions of an inch short of scoring, all but handing the win to the 49ers who simply had to run seven seconds off the clock.

  The delay of game penalty, and the subsequent defensive stop, gave the 49ers a first-round bye, home-field advantage throughout the playoffs, and some redemption for their overtime loss to Seattle in Week 10.

• Green Bay took care of business. All the Packers needed to secure a first-round bye was win what appeared to be a comical mismatch against Detroit. Naturally they fell behind, 14-0, in the second quarter, and were down, 20-13, with less than six minutes left. Even after tying the game, 20-20, they nearly threw things away: A pass by Aaron Rodgers was intercepted, giving the Lions a legitimate shot to win. Green Bay’s defense proceeded to hold for a three-and-out, and Rodgers drove his team down the field to set up Mason Crosby for a game-winning 33-yard field goal — just as the Packers, who came in as 12.5-point favorites, planned it.

• New England didn’t. The Patriots had as easy a path to a first-round bye as Green Bay, and an even more hapless opponent in the Dolphins. But Miami, getting some revenge for an ugly 43-0 loss in Week 2, delivered an enormous upset when Ryan Fitzpatrick hit tight end Mike Gesicki for a go-ahead 5-yard touchdown pass with 24 seconds left in the game. Quarterback Tom Brady, who contributed to his team’s failure with a pick-6 in the second quarter, will now play in the wild-card round for the first time since 2009, while the Chiefs, who beat the Chargers, will be able to rest until the divisional round.

• The Titans and the Eagles are playoff teams. It took until the regular season’s final day, but Tennessee and Philadelphia completed their impressive late-season surges by winning on Sunday and qualifying for the playoffs. The Titans, whose season turned around when Ryan Tannehill was named starting quarterback in Week 7, did not really need the win to secure the A.F.C.’s second wild card because Pittsburgh and Oakland lost their games. But the Eagles, who trailed Dallas in the N.F.C. East until a huge win last week, would have been eliminated by a loss thanks to the Cowboys’ blowout win over Washington.

• The Panthers wasted a terrific season. With 72 receiving yards in Carolina’s loss to New Orleans, Christian McCaffrey became just the third member of the N.F.L.’s 1,000-1,000 club, finishing the season with 1,387 rushing yards and 1,005 receiving yards. While Roger Craig was the centerpiece of a 10-6 49ers team when he founded the statistical club in 1985, and Marshall Faulk was changing football for a 13-3 Rams team on its way to a Super Bowl win in the 1999 season, McCaffrey’s Panthers, who dealt with a season-ending injury to quarterback Cam Newton and the firing of Coach Ron Rivera, finished with an ugly 5-11 record. In the end, McCaffrey’s 2,392 yards from scrimmage gave him the third most in an N.F.L. season, behind Faulk’s 2,429 and Chris Johnson’s 2,509.

• Jameis Winston stands alone. After Atlanta rallied to tie the score in regulation, the Buccaneers got the ball first in overtime. That gave Winston an opportunity to do something no other quarterback ever had, and Winston, a former No. 1 pick, took it. On the first play of the extra period, his pass was intercepted by Falcons linebacker Deion Jones, who ran it back 27 yards for an immediate game-winning touchdown. It was Winston’s 30th interception of the season, making him the first player to have a season with 30 or more passing touchdowns and 30 interceptions. That the interception was returned for a touchdown gave Winston an N.F.L.-record seven pick-6s for the season, and provided him a perfect bookend for his expiring rookie contract: Both his first and potentially his last passes for Tampa Bay were intercepted and returned for touchdowns.

The Wild-Card Round

Next week’s matchups have been set.

Saturday

No. 5 Buffalo at No. 4 Houston, 4:35 p.m., ABC and ESPN

No. 6 Tennessee at No. 3 New England, 8:15 p.m., CBS

Sunday

No. 6 Minnesota at No. 3 New Orleans, 1:05 p.m., Fox

No. 5 Seattle at No. 4 Philadelphia, 4:40 p.m., NBC

First-round byes: Baltimore, Kansas City, San Francisco, Green Bay

Top Passer: Dak Prescott

Prescott is seeking a huge new contract, and he will undoubtedly get it, but the amount of his production that came against terrible teams this season, and his inability to steer his team into the playoffs, shouldn’t be ignored.

Top Runner: Derrick Henry

Henry’s dominance in the second half of the season helped power his team to an unlikely playoff spot, and on the season’s final day he passed Cleveland’s Nick Chubb for a hard-earned rushing title. Gus Edwards of the Ravens deserves some attention as well, though, as the running back who is typically his team’s third option for carries behind Mark Ingram II and Lamar Jackson, provided the bulk of Baltimore’s offense in a somewhat surprising win over Pittsburgh. The Ravens broke a 41-year-old N.F.L. record by running for 3,296 yards as a team this season.

Top Receiver: DeVante Parker

As the season progressed it seemed like every noteworthy player on the Dolphins was either traded away or sustained a season-ending injury. Parker stuck around and on Sunday he helped lead his team to a shocking upset of the Patriots, giving Miami a nice ending to a trying season.

Cleveland Fires Freddie Kitchens

The Cleveland Browns were a trendy pick for a Super Bowl run after the team acquired wide receiver Odell Beckham Jr. and running back Kareem Hunt in the off-season, so it was not much of a surprise when the team followed up its 6-10 season by immediately firing Coach Freddie Kitchens.

Other coaches who could be on the way out on Monday, or soon after, include Jason Garrett of the Cowboys, Doug Marrone of the Jaguars and Pat Shurmur of the Giants, while neither the Redskins nor the Panthers are expected to retain their interim head coaches.

One* Sentence About Sunday’s Games

*Except when it takes more.

Chiefs 31, Chargers 21 A big win clinched a first-round bye for Kansas City, but it came with a huge cost as Juan Thornhill, a standout rookie defensive back, injured his knee and may be unavailable for the playoffs.

Packers 23, Lions 20 Green Bay did not lead at any point before Mason Crosby’s game-winning field goal as time expired — but that’s all that counts.

49ers 26, Seahawks 21 San Francisco had its last five games of the season come down to the final play, and has been dealing with numerous injuries on defense, but a first-round bye gives the 13-3 team a chance to get healthy as it seeks the sixth Super Bowl win in franchise history.

Dolphins 27, Patriots 24 “Nobody feels sorry for the Patriots not getting a first-round bye in the playoffs,” Patriots safety Devin McCourty said.

Saints 42, Panthers 10 Needing a win to stay alive in the race for a first-round bye, New Orleans had done enough to get there by the end of the first quarter — and then just kept going in a blowout. Drew Brees threw three touchdown passes, stretching his record to 547 for his career and putting him six ahead of Tom Brady before an off-season in which both future Hall of Famers may consider retirement.

Broncos 16, Raiders 15 A wild final drive by Oakland, which included a ball being simultaneously caught by a receiver and a defensive back (tie goes to the receiver, F.Y.I.), resulted in a touchdown and a 1-point deficit with just seven seconds remaining. Coach Jon Gruden decided to go for the win with a 2-point conversion, rather than tie the game with an extra point, and that decision blew up for the Raiders when quarterback Derek Carr’s pass was deflected to the ground at the line of scrimmage.

Cowboys 47, Redskins 16 In a game that did not end up mattering — Dallas needed Philadelphia to lose to the Giants for a chance at winning a division title — the Cowboys finally let their offense have some fun. Dak Prescott and Ezekiel Elliott both looked terrific, and the mystery of where they were last week in a loss to the Eagles will continue to haunt the team.

Eagles 34, Giants 17 The youthful Giants put up quite a fight for much of this game, but Philadelphia’s defense turned up the intensity, forcing a few turnovers and helping the team clinch a division title.

Bears 21, Vikings 19 Chicago’s 2018 season ended with a missed field-goal attempt in the playoffs, and its 2019 season ended with a go-ahead field goal by Eddy Pineiro with just 10 seconds remaining against a team with no real motivation to win. The stakes were far lower than last season, but progress is progress.

Jets 13, Bills 6 Buffalo did not have any incentive to win this game — it showed — and that minimal effort helped the Jets avoid a fourth consecutive season of double-digit losses.

Rams 31, Cardinals 24 It is nowhere near as good as a trip to the playoffs, but Los Angeles avoided a losing season thanks to a strong effort by quarterback Jared Goff, who outdueled Arizona’s Kyler Murray by throwing for 319 yards and three touchdowns.

Falcons 28, Buccaneers 22 Getting a win in overtime was ultimately meaningless, but along the way Atlanta ran a play in which Ty Sambrailo, a 315-pound offensive tackle, ran up the middle as an eligible receiver, deftly caught a pass from Matt Ryan in stride, and outran Tampa Bay’s defense into the end zone to deliver the N.F.L.’s seventh receiving touchdown by a 300-pound player this season — a record. The play went for 35 yards, breaking the previous record for reception length by a 300-pound player (25 yards, by tight end Kevin Brock in 2013).

Jaguars 38, Colts 20 There’s no telling what Jacksonville’s plans at quarterback will be next season, but Gardner Minshew closed this season on a high note, with 295 passing yards and touchdown passes to three different receivers.