Taylor Swift may not have had her BFF Brittany Mahomes by her side on Thursday night, but that didn't stop her from letting loose at the Chiefs game ... check out new video TMZ Sports has obtained from her evening in her suite seats -- she was going nuts!!

Swift -- who eschewed one of her normal chairs at Arrowhead Stadium next to Patrick Mahomes' wife for a spot adjacent to Travis Kelce's parents -- was seen throughout Kansas City's opener rooting on her man and his teammates vs. Baltimore very enthusiastically.

Before the start of the game, she could be seen pressing her hands against the luxury box's glass to get pumped up.

Later, after what appeared to be a big Rashee Rice play -- she threw up four fingers on each hand (presumably to match Rice's No. 4 jersey number) and did a little dance.

As the Chiefs continued to pad their lead against the Ravens ... she celebrated even further -- pressing her hands all over the glass. Fingerprints that were already there suggest it was hardly the first she celebrated in that manner.

Of course, things relaxed a bit for Taylor once the Chiefs officially won 27-20 ... as she was seen calmly enjoying some postgame time with her man.

It'll be a minute 'til the Chiefs take the field again -- their next matchup is Sept. 15 against the Bengals -- which is probably a good thing for Taylor following that hectic night.