Ryan erased a 10-6 deficit with 7:57 to go in the third quarter on the long scoring play, part of a performance that saw him throw for 187 yards on 16-of-28 passing.
Kroy Biermann sealed the fourth straight win for Atlanta (4-1) by returning an interception for a score late in the fourth quarter.
White ended the day with five receptions for 101 yards and Michael Turner rushed for 140 yards on 19 carries for the Falcons.
Seneca Wallace started at quarterback for Cleveland (1-4) but left late in the first half after suffering a right leg injury. Jack Delhomme entered and went 13-of-23 passing for 97 yards with two interceptions.