Trailing 31-21 after three quarters, Ryan engineered a 12-play, 80-yard drive capped by a 1-yard TD pass to Ovie Mughelli with 10:45 left, pulling the Falcons to within four points.
Ryan (17-of-28, 195 yards) again drove the Falcons 80 yards with Michael Turner scoring on a 3-yard run with 4:46 left, putting Atlanta ahead for good.
Turner carried the ball 21 times for 114 yards, and Tony Gonzalez made seven grabs for 83 yards and a pair of scores for Atlanta (1-1).
Michael Vick completed 19-of-28 passes for 242 yards and two scores before being knocked out of the game in the third quarter. The signal-caller was hit by Falcons safety William Moore and fell awkwardly into teammate Todd Herremans.
Third-string quarterback Mike Kafka took over and went 7-of-9 for 72 yards as the Eagles (1-1) failed in a last-ditch drive.
Jeremy Maclin hauled down 13 passes for 171 yards and two TDs but dropped a pass on a fourth-down play during the Eagles' final possession.