Cowboys Take Giant Step With 21-16 Win : NFC: Aikman’s touchdown pass to Irvin with 2:13 left puts Dallas over .500 for the first time under Johnson.

IRVING, Tex. —  Troy Aikman completed a 23-yard touchdown pass to Michael Irvin with 2:13 left and the Dallas Cowboys beat the New York Giants, 21-16, Sunday for their first victory over the Giants since 1987.

“We took a big step as a team, as a franchise today,” said Jimmy Johnson, who had been 0-4 against the Giants since he left the University of Miami to coach the Cowboys. “It was a very big step.”

Dallas (3-2) had not been over .500 since Johnson became the coach three years ago.

“There is no question that this is the biggest victory,” Aikman said. “It was one of the teams we needed to beat to establish ourselves. I just hope I can play here long enough where a victory over the Giants won’t be considered a novelty.”

The stumbling Giants (2-3) not only lost the game but also linebacker Lawrence Taylor, who tore a ligament in his left thumb early in the fourth quarter and missed Dallas’ game-winning, 84-yard drive.

“He says he’ll be able to play next week,” Giant Coach Ray Handley said. “It’s pretty painful.”

The Giants already had lost to the Chicago Bears and the Rams.

“This was a disheartening loss,” Handley said. “Now we need help. But you can still lose three games and go to the Super Bowl. We have dug ourselves a hole.”

Dallas took a 14-3 lead in the third quarter. The Giants went ahead, 16-14, on Jeff Hostetler’s 19-yard touchdown pass to a diving Stephen Baker with 5:41 left. The Cowboys then rallied and held on as Issiac Holt intercepted Hostetler’s pass for Baker in the Dallas end zone with 1:11 to play.

Dallas had lost six in a row against the Giants since a 33-24 victory at Texas Stadium in 1987. It appeared as if the Cowboys would lose again until Aikman led the comeback.

The Cowboys got the ball on their own 16 with 5:41 left. After an incompletion, Aikman completed a 13-yard pass to Alexander Wright and a 30-yarder to Irvin, moving the ball to Giants’ 41.

Emmitt Smith ran two yards and Aikman threw passes of five and 13 yards to tight end Jay Novacek, bringing the Cowboys to the 21. After a two-yard loss by Smith, Aikman threw over the middle to Irvin, who caught the ball at the four and broke Mark Collins’ tackle to score standing up.

“Michael Irvin is a winner, and that’s why he makes plays like that,” Johnson said. “He did a great job of believing in himself after dropping a pass.”

Said Irvin: “Collins was trying to tackle the ball instead of tackling me. It was the kind of play you dream about.”

But the Giants almost came back. Hostetler drove them to the Cowboy 30 before Holt intercepted a pass to seal the victory.

Baker’s touchdown catch that put the Giants ahead, 16-14, was somewhat controversial. It wasn’t ruled good until replay official Bill Stanley studied the fingertip grab and decided he caught it just above the Texas Stadium carpet.

“Troy did a great job of bringing us back,” Johnson said. “He made some big plays. You have to make big plays to beat a team like the Giants. It’s the best team effort we ever had in a spot like that.”

Aikman completed 20 of 27 passes for 277 yards, and Hostetler completed 28 of 34 passes for 368.

“We moved the ball all over the field and didn’t have anything to show for it,” Hostetler said. “We don’t want to panic yet, but this thing is getting close.”

New York cornerback Everson Walls blamed the Giants’ defense.

“Our offense played a hell of a game,” he said. “but the defense didn’t play well.”