A soaking rain finally stopped at halftime, and the Giants finally started, turning a no-hope, 16-point third-quarter deficit into a Monday Night Football game with enough twists and turns for a whole season.

After a wild exchange of field goals in the final 11 seconds sent the game into overtime, the Cowboys won, 35-32, on a 25-yard field goal by Billy Cundiff. It was Cundiff's seventh field goal of the game, tying an N.F.L. record.

It overshadowed a thrilling comeback by the Giants, who trailed, 23-7, in the third quarter. Quarterback Kerry Collins shook off a miserable first half with two interceptions and led the Giants' comeback behind a makeshift offensive line featuring three rookies. Collins threw touchdown passes to tight end Jeremy Shockey and Amani Toomer in the fourth quarter to pull the Giants into a 29-29 tie with 6:20 left.

The Giants thought the comeback was complete when Matt Bryant kicked a 30-yard field goal with 11 seconds left. But Bryant's ensuing kickoff skidded out of bounds, giving the Cowboys the ball at the 40. Quarterback Quincy Carter threw a 36-yard pass to Antonio Bryant, and Cundiff kicked a 52-yard field goal as time expired to send the game into overtime.

Until the Giants' comeback, it was nearly an unblemished coming-out party for the Cowboys' quarterback and their coach. Bill Parcells, who coached the Giants franchise to two Super Bowls in the early 1990s and roamed these sidelines for three years as the Jets' coach, won his first game since taking over as the Cowboys' coach.

On the field, though, the stars were Cundiff and Carter, the much-maligned quarterback Parcells installed in the starting job. Carter led the Cowboys on three scoring drives in the first half, scoring a touchdown on an 8-yard scramble, and driving them to three more field goals in the second half as the Cowboys kept pulling away from the Giants. Carter, who was 25 of 40 for 322 yards passing, spread big plays among his three receivers, Joey Galloway, Terry Glenn and Bryant, when the Cowboys needed them most.

But the Giants finally started matching Dallas with big plays in the fourth quarter. The touchdown pass to Shockey was the end of a 69-yard drive with 9:54 left. Toomer's touchdown, a 20-yarder, completed a three-play, 64-yard drive with 6:20 left. The Giants had three tries at the 2-point conversion because Dallas was twice called for pass interference, and they scored on the third attempt on a run by Tiki Barber.

At first, the Giants' defense seemed ready to make up for whatever struggles the offense might have.

The Giants' first two drives of the game went nowhere, but cornerback Ralph Brown scored the first points when he stepped in front of Galloway and returned an interception of Carter 29 yards for an easy touchdown with 7:21 left in the first quarter.

The Cowboys, however, got their offense going on the next drive. Carter hit Glenn with a 20-yard pass to the Giants' 37, then turned to the running game. Troy Hambrick had runs of 12 yards and 7 yards, and Richie Anderson ran for 11 more to the Giants' 7. After the Cowboys lost a yard on the next run, Carter dropped back to pass, then scrambled for a touchdown from the 8. That tied the game at 7-7 with 3:06 left in the first quarter.

The Giants' offensive woes already included giving up two sacks of Collins, one resulting in a fumble that the Giants recovered. Then they added a fumble by Barber at the Giants' 35-yard line. Dallas linebacker Dat Nguyen recovered it, and the Cowboys used the possession to take a 10-7 lead with a 37-yard field goal by Billy Cundiff.

The Giants' next drive featured a busted running play in which Barber ran into the back of his blockers and a long pass dropped by tight end Jeremy Shockey on third down.

The Cowboys drove 30 yards and got a 49-yard field goal by Cundiff for a 13-7 lead. The big gain was on a 21-yard pass from Carter to Galloway to the Giants' 36. But with a running game going nowhere and Collins limited to a quick-drop passing game, the Giants were going from bad to worse. The Cowboys responded by overplaying the quick slant routes the Giants' receivers were running.

Cowboys linebacker Al Singleton read one of those passes and intercepted Collins, running it back 41 yards for a touchdown and a 20-7 lead with 3:05 left in the half.

Collins finally connected for a big gain on the Giants' ensuing drive, a 40-yard pass to Amani Toomer to the Dallas 32. But four plays later, Collins threw another interception, this one by cornerback Terence Newman at the 20.

At halftime, the Giants' statistics read like their worst nightmare. They had 14 rushing yards. Collins was 7 of 21 for 105 yards. Their best offensive drive ended in an interception. They had three turnovers and five first downs.

Halftime gave them a short escape - and an end to the rain - but the second half brought no immediate relief. The Giants' kickoff bounced out of bounds, giving the Cowboys the ball at their 40. They needed only 36 yards for Cundiff to kick a 42-yard field goal with 11 minutes left in the third, giving Dallas a 23-7 lead. Again, Carter was doing all the damage, with big completions to Bryant (25 yards) and Jason Witten (15 yards).

The Giants' offense started moving on the first drive of the second half. The big play was a 38-yard penalty, when Dallas safety Roy Williams was called for pass interference in the end zone while trying to defend Toomer, who finished with 7 receptions for 126 yards. The play was a Barber-to-Ike Hilliard reverse, and Hilliard threw it back to Collins, who threw deep to Toomer.

With the ball at the 1, Shockey dropped a pass in the end zone and Barber was thrown for a 4-yard loss. Collins then passed to Hilliard for a 5-yard touchdown, cutting the Cowboys' lead to 23-14 with 8:11 left in the third.

The Giants still could not stop the Cowboys' offense, which drove for another field goal by Cundiff that made the lead 26-14 with 4:53 left.