The Giants (6-2) built a 23-0 halftime lead but then had to fend off a furious Cowboys rally down the stretch to record their third consecutive win and fourth straight in Dallas.
Two Tynes field goals in the fourth quarter had given the Giants a five-point lead, but the Cowboys momentarily looked to have grabbed the advantage when Tony Romo hooked up with Dez Bryant on an apparent 37-yard TD toss with 10 seconds left.
The play, however, was overturned when replays showed Bryant's hand came down beyond the end zone, and New York got the win when the Cowboys' quarterback missed on two final pass attempts.
Jason Pierre-Paul returned an interception for a touchdown and Stevie Brown supplied two pickoffs and a fumble recovery in New York's victory.
Romo amassed a career-best 437 yards on 36-of-62 efficiency, but surrendered four interceptions for Dallas (3-4).
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys