Glennon made good on 20-of-23 passes. His favorite target was Vincent Jackson, who hauled down 10 throws for 165 yards and a score as Tampa Bay (2-8) won a second straight after starting the season with eight losses in a row.
Bobby Rainey led the Bucs' ground game, racking up 163 yards with two TDs on 30 carries.
The Falcons (2-8), meanwhile, stumbled to a fourth straight loss.
Matt Ryan was held to 19-for-36 passing for 254 yards, two touchdowns and two interceptions.
Harry Douglas made six grabs for 134 yards and a score for Atlanta.