Elliott, who learned Friday he likely will be eligible to play all season thanks to the courts, finished with 104 yards on 24 tough carries.
Two of Prescott’s three losses a year ago came against the Giants, but he managed to beat this NFC East rival without his best performance, completing 24 of 39 passes for 268 yards.
Witten became Dallas' all-time leader in receiving yards and had the Cowboys' only touchdown, as 12-yarder with 1 minute, 41 seconds left in the first half.
Bryant, limited to 18 yards and two catches in the meetings against New York last year, caught two passes for 43 yards.
Yet none of them were the story.
The story Sunday was the Cowboys' defense, a group that had been questioned before they'd even played a game.
The Giants did not have wide receiver Odell Beckham Jr. because of an ankle injury, but the defense allowed just two first downs in the first half, sacked Eli Manning three times and picked him off once.
Consider: The Cowboys ran 47 offensive plays in the first half while the Giants had 49 yards.
DeMarcus Lawrence, who had one sack last season, matched his 2016 season total on the first series of this season. Charles Tapper, who did not play last season because of a back injury, had a critical third-quarter sack with New York at the Dallas 4 that forced the Giants to settle for a field goal.
"Ultimately you are measured by how many points you give up," coach Jason Garrett said. "For us to hold them to three points, they've got a lot of weapons on that offense. Obviously the quarterback is outstanding. So for us to be able to do that against that offense, I thought that was impressive. We minimized the big plays. We didn't let them get the run game going. I just for the most part those were the big factors."
The Cowboys’ offense wasn’t efficient, but after the Brown takeaway they ate nearly six minutes off the clock to effectively put the game away. Elliott carries seven times for 30 yards. Alfred Morris carried twice for minus-1 yard. Prescott completed his seventh pass of the night to Witten. Dan Bailey ended the drive with his fourth field goal, a 36-yarder with 1:55 to play.
The Giants picked up meaningless yards on their final drive that padded some stats, but on this night the Cowboys’ defense told the story.
The Cowboys will need more of that if they want to repeat as NFC East champions in 2017.