A subway station in San Francisco turned into the scene of a police shooting when cops gunned down a man they say was armed with a firearm ... and it's all on video.

New police body cam footage shows SFPD officers unleashing a hail of bullets on the suspect as he walks through the underground Powell Street BART station.

Cops say the guy was carrying a gun and had been leading police on a chase through the city before he was shot in front of commuters, who had to duck for cover.

The suspect, who cops identified as 30-year-old Justin Alderman, gets off an escalator right before police open fire ... and the bullets send him falling to the ground with what SFPD described as non-life threatening injuries.

Police say this all started when patrol officers spotted the man sleeping in a stolen white BMW around 10 AM on Sept. 13, with a gun in plain view next to him in the passenger seat.

SFPD says the suspect ran and led them on a winding chase that ended at the BART station ... and police say they recovered a revolver loaded with 5 bullets.