Ryan completed 23-of-28 passes for 270 yards with two of his scoring passes going to Julio Jones as the Falcons (12-2) gained revenge for a loss to the Giants in last year's NFC wild-card playoff contest.
Jones finished with 74 yards on six catches.
Atlanta's defense stopped the Giants on downs three times in handing New York its first regular-season shutout loss in 16 years.
Eli Manning was intercepted twice in the first half, ending with just 161 aerial yards on 14-of-26 efficiency for New York (8-6).
With their fourth loss in six games, the Giants fell into a three-way tie with the Dallas Cowboys and Washington Redskins atop the NFC East.