Dallas received a scare when rookie linebacker Leighton Vander Esch stayed down after making a tackle in the fourth quarter.
Vander Esch, though, was kicked in the left shin and appears OK.
The first-round pick began limping after Evan Engram made a 51-yard catch. On the next play, Vander Esch needed medical attention on the field after he and linebacker Jaylon Smith got tangled while combining on a tackle.
Joe Thomas, not Sean Lee, replaced Vander Esch. The Cowboys have Lee on a pitch count, hoping to keep his snaps around 20 as he works his way back from a hamstring injury.
The Giants took the 25-21 lead with 10:38 left on a 2-yard touchdown run by Wayne Gallman.
Engram scored on a 6-yard pass from Eli Manning in the third quarter and caught the two-point conversion.
But the Cowboys since have answered with a 1-yard touchdown run by Rod Smith. Dallas leads 28-25 with 9:11 left, and Dak Prescott remains in the game.