Elliott made it to the field after a court injunction stayed a six-game suspension from the N.F.L. — a penalty based on a 2016 accusation that Elliott had beaten his former girlfriend. Beckham ran some sprints in the pregame warm-up, but ultimately he could not play because of an ankle sprain sustained about three weeks ago.
Beckham’s absence may have affected the game’s outcome — the Giants’ offense looked flustered and feeble. But Elliott’s presence unquestionably influenced the result, as he knifed through the Giants’ vaunted defensive front for 104 rushing yards on 24 carries and bewildered the secondary for 36 more yards on five pass receptions.
For the Cowboys, this victory helped wipe away the bad taste of the losses to the Giants last year, and of the disappointingly abrupt end to their postseason in January.
For the Giants, the game was a humiliating defeat that left Coach Ben McAdoo uncharacteristically and caustically critical of his team.
“No part of our offense was functional tonight,” McAdoo said.
Asked why various players, especially on offense, had not been able to get into the flow of the game, McAdoo interrupted to reply: “We weren’t able to get anyone going. No one got going.”
At least part of the answer appeared to be Dallas’s strategies. The Cowboys had tried to stop the Giants’ passing game last year mostly with man-to-man defense. They knew that they needed to make a change and that the Giants had not altered the schemes of their offense and defense.
“This year, they played less man and more zone, especially on third down,” said Giants quarterback Eli Manning. “They had some new stuff — a lot of good calls ready for us. And it forced me to go to second and third receivers. We have adjustments, but we didn’t convert them.”
Manning completed 29 of 38 passes, but few of them on third down — when the Giants gained a first down only a third of the time.
The Giants’ bumbling offensive fit well into this disorderly game. Prescott proved his dazzling rookie season had not been an aberration with precise passing worthy of a longtime player. He completed 24 of 39 passes for 268 yards.
Prescott proved to be an elusive runner, too. On one play, he stepped around attempted tackles by Jason Pierre-Paul and Olivier Vernon, the Giants’ feared defensive ends, for a 17-yard scramble and a critical first down. Prescott finished with 24 rushing yards.
The Dallas defense, which was not considered a strength last year or during the 2017 preseason, repeatedly swarmed and badgered Manning in the passing pocket. The much-maligned Giants offensive line, a major liability last year, seemed overmatched play after play. In the off-season, the Giants chose not to acquire a new lineman to bolster the unit.
That decision appeared to be a glaring gaffe on Sunday.
Pressed to explain the Giants’ continuing troubles on the offensive line, McAdoo tried to scatter the blame.
“You can’t focus on one part,” he said. “Can’t put it in one place only. We have a lot of work to do.”
But McAdoo warned against overemphasizing the Giants problems: “It is one game of 16. You have to be careful.”
Dallas was happy to be looking forward. “A nice way to start the season,” Cowboys Coach Jason Garrett said, smiling. “There were a lot of good things out there for us to build on.”
The Giants troubles were many. On the run most of the time, Manning had a difficult night. He also seemed out of sync with his new wide receiver, Brandon Marshall, who was rarely the quarterback’s target. Marshall had one catch for 10 yards.
“He’s a weapon,” Manning said. “We’ve got to get him involved.”
After a first half in which they gained just 49 yards, the Giants trailed by 16-0. The deficit might have been three touchdowns or more, but the Cowboys had hurt themselves several times, stalling promising drives.
Beginning the third quarter, the Giants rallied as Manning completed eight successive passes to bring his team to the Dallas 5-yard line. But the Giants’ porous offensive line faltered again, with left tackle Ereck Flowers allowing the Cowboys’ Charles Tapper to slice through almost untouched for a 9-yard sack.
A potentially morale-boosting touchdown became a 25-yard field goal instead, by the Giants’ rookie kicker Aldrick Rosas.
Dallas thwarted each of the Giants’ drives thereafter, most notably when defensive back Anthony Brown intercepted a deep Manning pass with 5 minutes 48 seconds remaining in the game.
“It’s a tough loss, we know all about this rivalry,” Giants defensive back Dominique Rodgers-Cromartie said in the quiet locker room. “It hurts, no doubt. But we’ll see them again. You can count on that. We’ll be there.”