The Cowboys were first off the mark when Dan Bailey kicked a 30-yard field goal early in the first quarter, but it proved to be an extremely tight in the early stages of the contest.
Josh Brown kicked the Giants level with just over two minutes left on the clock in the first quarter, although the Dallas had George Selvie to thank for sacking Eli Manning as he scouted a touchdown pass.
Another kick from Bailey edged Dallas back in front, before Tony Romo fired a 15-yard pass for Jason Witten to score the first touchdown of the game with three minutes of the second quarter remaining.
The home side led 13-10 at half time and soon stretched their advantage early in the third quarter, with Nick Hayden stripping a beleaguered David Wilson of possession to allow Barry Church to pickup for an easy score.
Jason Garrett's side went further ahead when Romo found in the endzone Witten once again, before Bailey kicked the extra point.
The Giants got themselves back in the game when Cruz rode a mid-air hit from Will Allen to drive over the goalline.
Leading 27-10 heading into the fourth quarter, Bailey smashed a 45-yard field goal between the posts to extend the Cowboys' cushion to 20 points.
However, the Giants refused to lie down, as Manning and Cruz combined for the third time in the game to pull within six of the Cowboys. Their defense was also standing firm, sacking Romo twice in quick succession.
Any hopes of completing a turnaround were dashed with one minute and 50 seconds of the game remaining.
Manning went looking for Da'Rel Scott but the running back, who was not looking at the ball, inadvertently flicked it into the hands of Brandon Carr, who then skipped gleefully over the line amid the din of the 85,348 fans in attendance.
The Giants still had time to grab one touchdown back, with Manning finding Brandon Myers to give them a slim chance of recovery.
With 10 seconds left on the clock, Sean Lee pounced on the ball to win possession for the Cowboys, allowing Romo to take a knee and seal their first win against the Giants in the AT&T Stadium.