Kevin Ogletree was the recipient on two occasions, with fellow wide receiver Miles Austin on the end of a third as the Cowboys stretched their lead to 24-10 in front of 82,287 fans - a record crowd at MetLife Stadium for a Giants game.
New York reduced the deficit with 2:36 remaining in the fourth quarter when Eli Manning and Martellus Bennett connected, but they could make no further inroads.
The game was a rematch of the Jan 1 game won by the Giants that ultimately gave them the NFC East title. The Cowboys defended solidly as they made three sacks and six pressures to frustrate the Super Bowl champions who lost the season opener for the first time in nine games.
Ogletree also impressed for the Cowboys as he made114 yards on eight catches and had 25 receptions for 294 yards. The New York native confessed his surprise at the confident manner of his side's victory and enjoyed his team's performance at the MetLife Stadium.
"A huge emphasis for us was big plays," said Ogletree.
"I don't want the focus to be on me too much, but I am very, very humbled and appreciative of how we played today [Wednesday].
"I'm close to home, so it's a good feeling. But Dallas is my home now."