Ryan, playing without wide receivers Julio Jones (foot surgery) and Roddy White (hamstring), instead went to Harry Douglas, who racked up a career-best 149 yards with a touchdown on seven catches for Atlanta (2-4).
Running back Jacquizz Rodgers also stepped up his receiving game, making eight grabs for 46 yards and a pair of scores as the Falcons broke a three-game skid against AFC East opponents.
Tampa Bay (0-6) remained winless despite a good game from Mike Glennon, who made good on 26-of-44 pass attempts for 256 yards and two touchdowns.
Vincent Jackson caught both scoring strikes, finishing with 10 receptions on his way to 138 yards for the Buccaneers.
Celebrity Breakups and divorces of 2014 [PHOTOS]