Bowman's pick-off and touchdown with 1:31 to play stopped the Falcons at the 49ers' 10-yard line and enabled San Francisco (11-4) to hold on for a win in what could be the team's final game at Candlestick Park.
The victory also kept the Niners' hopes for a No. 1 seed in the NFC alive.
It wasn't easy, however, as Matt Ryan led a late surge that nearly rallied Atlanta from a 10-point deficit.
He hooked up with Tony Gonzalez on a 2-yard TD pass with 2:09 left, cutting San Francisco's lead to 27-24.
The Falcons then got the ball back with a successful onside kick and moved deep into 49ers territory before Ryan's pass to Harry Douglas was deflected by Tramaine Brock.
Bowman grabbed the ball in midair and ran the other way untouched for a scintillating touchdown.