Ryan's 2-yard toss to Peelle with 2:01 left in the third quarter erased a one-point deficit and put the Falcons (8-2) ahead for good. Atlanta added 10 more points in the fourth period to seal the win.
Matt Ryan amassed 253 yards and a pair of touchdowns and Michael Turner rushed for 131 yards. Turner got the Falcons' final points on a 39-yard TD run.
The Rams (4-6) went up 17-16 on Sam Bradford's 13-yard scoring strike to Brandon Gibson, but he could get St. Louis no closer.
Bradford finished 27-of-42 passing for 233 yards, two TDs and an interception, his first pickoff in 170 attempts.