IRVING, TEXAS ? Bill Parcells was on his way to the team bus in the wee hours Tuesday morning, still smiling from an incredible first victory as coach of the Dallas Cowboys and thrilled to have shared it with so many friends.

Then he clicked on his cell phone and listened to about eight messages. All were congratulatory, though most aren’t fit for print.

“Friendly obscene,” he described them, adding they were hilarious.

Bob Knight called later and praised a rookie for a heady play during crunch time. When Carolina offensive coordinator Dan Henning phoned, he skipped hello and went straight to the Xs and Os behind an important pass.

“He just called the play the way we call it in the huddle,” Parcells said of his former assistant.

For Parcells, the jokes were funnier and the questions easier to answer in the afterglow of the 35-32 overtime victory against the New York Giants that began Monday night and ended about 1 a.m. Tuesday.

Dallas surprisingly led by 13 points at halftime and by 15 in the fourth quarter. Then the Giants got hot, the Cowboys got cold and New York led with 11 seconds left. All the Giants needed was a squib kickoff that would give Dallas time for only a desperation pass.

But the ball curled out of bounds at the one, a penalty that let the Cowboys start at the 40. A quick sideline pass to Antonio Bryant — the one Henning knew was coming — set up Billy Cundiff’s career-long 52-yard field goal as time expired.

Cundiff made a 25-yarder in overtime, giving him an NFL-record-tying seven in one game and making Parcells 1-1 in his new job.

Dallas coach Bill Parcells, center, and tight end James Whalen (81) celebrate a catch by Terry Glenn, bottom, that helped set up kicker Billy Cundiff's game-winning field goal in overtime. The Cowboys defeated the New York Giants, 35-32, Monday night in East Rutherford, N.J.

“That,” Parcells said, “was a good win.”

The in-game circumstances were remarkable enough.

Doing it on the road, against a division rival, on a Monday night, in a hostile environment — one that happens to have been Parcells’ home stadium for 11 of his previous 15 seasons as a head coach — and with dozens of his former players there … well, it was enough to almost make Parcells choke up.

Saying he didn’t want to be too sentimental, Parcells made it clear how much it meant to him that Lawrence Taylor, O.J. Anderson, Mark Bavaro and several other players he led to two Super Bowls with the Giants stopped by the visiting locker room after the game.

“That’s really why I coach — for that,” Parcells said. “When you see those kids you had and they’re 45, 46 years old now and they’re coming and hugging you, saying, ‘Hey, go do your work. Get your job done,’ it means a lot to you. It makes you feel special.”

Parcells knows he’s a long way from building that bond with the Cowboys. But Monday night was a great start.

While these players already have the utmost respect for Parcells, his stock still went up considering the game was decided by the kind of unique circumstances he spent much of training camp preparing them to handle.

“It’s really ironic that I’ve been trying to emphasize these situations and a game so early in the season will come down to one of those very situations that we’ve spent a lot of time on,” he said.

Players were off Tuesday and won’t practice today. They’ll meet, though, and they’re sure to hear about more negatives than positives, such as blowing a lead for a second straight game, with the defense getting pushed around in both. And the fact Cundiff was used so much means the offense was stopped short on too many drives.

Parcells also said there were about five players who “didn’t show up,” and he plans to meet with each of them.

“We’ve got some things we’ve got to get fixed this week,” Parcells said. “Because if we don’t get it fixed, we’re going to have a lot of trouble.”

Parcells said it was too early to know whether this game would prove to be a turning point. Still, the timing is good as Dallas has a bye this weekend, which means more time to savor the victory.

“It’s a lot easier to talk to your team in a critical way when the sensitivity level is lower, which it is now, because no one is responsible for losing,” he said. “You can talk more frankly and more adamantly and more candidly without worry of offending people. … Coming off a good win enhances your ability to make those points without finger-pointing.”

Best of all, though, simply is being 1-1.

“If you’re 0-2, you don’t ever know if you’re going to win,” Parcells said. “You can go 0-16 or 1-15. You can do that easily. There’s not a team in the league that couldn’t beat us if we don’t play pretty good.”