Henery's decisive kick was his third field goal of the game and handed the Eagles (3-1) a victory following last week's loss to Arizona.
Eli Manning led the Giants (2-2) on a last-chance drive but it stalled when receiver Ramses Barden was whistled for offensive pass interference. Lawrence Tynes missed a 54-yard field goal attempt and the Eagles' win was assured.
LeSean McCoy ran for 123 yards on 23 carries and Vick toted the ball six times for 49 yards.
Manning finished 24-of-42 passing for 309 yards, two TDs and an interception.
Domenik Hixon and Victor Cruz combined for 223 yards and a score on 15 catches for the Giants.