They scored 45 points -- the most in a season opener since 1971.
Patrick Crayton got the start in place of Glenn and caught three passes for 51 yards.
Second-year player Sam Hurd moved up to the No. 3 spot and caught a 51-yard touchdown pass to seal the 45-35 victory in the fourth quarter.
But the situation with Glenn remains curious. Glenn was sidelined for the preseason after undergoing arthroscopic knee surgery Aug. 1.
He returned to practice last week in hopes of playing in the season opener but suffered a setback when suffered damage to the articular cartilage in his right knee.
Now Glenn has some decisions to make.
He could have another scope to alleviate the problem and be back in five or six weeks and continue to chase his Super Bowl dream.
Or he could have season-ending and possibly career-ending microfracture surgery.
He spent Tuesday in Birmingham, Ala., to get a second opinion from noted Dr. James Andrews.
"Obviously, it's a tough decision for him, but he knows all the details," head coach Wade Phillips said.
The final decision will be Glenn's and his alone, said Cowboys owner Jerry Jones. Jones said they will keep a roster spot open for Glenn as long as it takes and will not rush him into a decision.
"He's got some options," Jones said. "He can take that cartilage out, spend four or five weeks and then take another look at it. I think he's leaning that way, but I think it's something that his decision will be evolving here over the next few weeks."
* WR Terrell Owens denies that he gave Giants defensive back Gibril Wilson an obscene hand gesture, prompting a late hit following Owens' 47-yard touchdown in the fourth quarter. Owens said he extended his index finger, signaling no. 1. Wilson says it was something else.
* TE Jason Witten caught six passes for 116 yards. It was his first 100 yard receiving game since 2004. But most impressive according to coach Wade Phillips was Witten's play as a blocker. Phillips said he was downright dominant.
* QB Tony Romo went a long way toward quieting any remaining doubters with a career high 345 yards passing and accounting for five touchdowns in the season opener. But he knows he still has his critics. He said he is not going to worry and will enjoy the journey.
"If you perform well, nothing else matters," Romo said. "If you don't perform well, then that opens you up to criticism in a lot of area. I learned a long time ago it's about the journey, not the destination. So I am going to enjoy life as a whole. The game was part of an incredible experience I am going to enjoy having."
* RB Marion Barber had 11 carries for 65 yards in the season opener, fanning the flames of a running back controversy. However, Julius Jones had 14 carries for 66 yards and the Cowboys liked the overall production from the tandem.
* WR Sam Hurd caught his first career touchdown pass in the season opener against the Giants, a game-clinching 51-yarder in the fourth quarter. Fellow receiver Patrick Crayton said he probably slept with the football after the game.
* CB Terence Newman sat out the season opener against the Giants with a tear in his right plantar fascia. He will try to practice on Wednesday but the Cowboys are bracing for the fact that he might miss two or three games.
* NT Jason Ferguson is set for season-ending surgery to repair a torn biceps muscle. Jay Ratliff, a defensive end, will replace him in the starting lineup. The Cowboys might sign Remi Ayodele to replace Ayodele on the roster. Don't be surprised if the Cowboys take a look at former Bears defensive tackle Tank Johnson.
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