Manning hit wide receiver Plaxico Burress with a 50-yard bomb on the fifth play of the match at Texas Stadium as the Giants marched to their third successive win, and to the top of the NFC East division.
25-year-old Manning threw 12 completions from 26 attempts for 189 yards, with his second touchdown pass going to tight end Jeremy Shockey early in the third quarter.
Cowboys quarterback Drew Bledsoe struggled again, and although he threw 7 from 12 for 111 yards with one interception, he was replaced by Tony Romo in the second half, who threw two touchdown passes and three interceptions.
One of Romo's interceptions was returned 96 yards for a touchdown by Giants defensive back Kevin Dockery in the fourth quarter to seal the match for New York.
"That was really a poor performance," Dallas coach Bill Parcells said.
"A recipe for disaster. It was a real bad performance. And there's really no excuse for it."
11-season veteran Terrell Owens caught six passes for 98 yards and one touchdown for the Cowboys and got far more involved in the game when Romo was at quarterback than he was with Bledsoe.
The Giants shot out to a 12 point lead early in the second quarter, however Bledsoe orchestrated a 10-play, 80-yard touchdown drive, rushing over himself to leave the Giants 12-7 ahead at halftime.
After Shockey's touchdown, running back Brandon Jacobs scored on a three-yard rush to put the Giants up by 19, but Dallas rallied in the fourth quarter to make the game interesting.
Romo hit Owens to reduce the deficit to 26-15, which got the sell-out crowd pumped up for a possible comeback, but Jay Feely added a 32-yard field goal before Dockery's long range touchdown return.
Touchdown: wide receiver Plaxico
Burress (L) scores for New York
Romo, who finished with 14 from 25 for 227 yards, found Patrick Clayton with a 53-yard touchdown pass late in the match to complete the scoring.
Arrington does Achilles
LaVar Arrington, Giants linebacker, was credited with a safety late in the first quarter when he sacked Bledsoe in the endzone but his game, and season, ended after he tore an Achilles tendon when chasing down Dallas' Julius Jones on a running play.
"That's the one sad thing about this game, when you lose a player," Giants coach Tom Coughlin said.
"The guy was improving week in and week out.
"Hopefully we'll keep winning. This is our third win on the road now. We just fed off each other," added Coughlin.
Doctors told Arrington he could be out for six months but should be able to regain full fitness.
"It felt like somebody hit me in the back of the leg, but there was nobody there," Arrington said.
"When I went down, I knew it. I just didn't feel right."
The Giants now face Tampa Bay at home on Sunday while the Cowboys travel to Carolina for another Monday night football clash next week.