The Cowboys (2-4) have lost four games in a row and fumbled away a chance at a game-tying drive in the final minute of the game when wide receiver Cole Beasley fumbled a punt.
It was the first win for the Giants (4-3) in the NFC East rivalry in the past six meetings. Dwayne Harris' 100-yard kickoff return for a touchdown gave the Giants their winning margin.
Harris, who spent the first four years of his career with the Cowboys, tied a Giants franchise record for the longest kickoff return for a touchdown, last set by Clarence Childs on Dec. 6, 1964.
Cowboys quarterback Matt Cassel was picked off three times by the Giants, twice by cornerback Dominique Rodgers-Cromartie, who had a 58-yard pick-6 in the third quarter to the Giants a 17-13 lead.
Giants safety Brandon Meriweather intercepted Cassel at the 1-yard line to snuff out a Cowboys scoring drive.
The Cowboys jumped out to an immediate 3-0 lead on the first of kicker Dan Bailey's two field goals.
Dallas running back Darren McFadden, who rushed for 152 yards on 29 carries, scored the first touchdown for the Cowboys.
The Giants' lethargic running game got a much-needed shot of adrenaline thanks to the fresh legs of fourth-string running back Orleans Darkwa, who rushed for 41 yards on four carries, including a touchdown with 11:10 left in the second quarter.
Darkwa, who finished with 48 yards on eight carries, and running back Shane Vereen, whose 39-yard run in the third quarter helped set up Josh Brown's 34-yard field goal, helped snap streak of six games in which the Giants ground game failed to reach the 100-yard mark.
Cassel delivered a beautiful 25-yard pass from to receiver Devin Street in the back of the endzone for a touchdown to cap a 9-play, 80-yard drive, but it was 20-20 for only the length of the television break. Harris returned the ensuing kickoff 100 yards for the game-winner.
The Giants are at New Orleans next week and Tampa Bay the following week.
The Cowboys (2-4) are home for back-to-back home games against Seattle and Philadelphia.
NOTES: Giants kicker Josh Brown's two field goals gave him 19 straight, breaking his previous franchise record of 17. ... The loss marked the end of the Cowboys five-game winning streak against the Giants and their four-game streak against the Giants in games played at MetLife Stadium. ... The Giants completed the season series against Dallas without turning the ball over for the first time in head coach Tom Coughlin's tenure. Quarterback Eli Manning has tossed just one interception in his last five regular-season starts vs. the Cowboys, that one pick coming on a 31-28 loss on Nov. 23, 2014.