IRVING, TEX., NOV. 3 -- There might not have been a single team in the National Football League with as many problems as the Dallas Cowboys.

Infighting had rocked the team during and since the strike, the fans had fallen in love with the replacement Rhinestone Cowboys and scorned the veterans, Tony Dorsett and Herschel Walker had said one backfield wasn't big enough to hold both of them, and the Eagles had stepped on their faces a week ago.

The whole league wanted a piece of the Cowboys and, worst of all, it appeared Dallas had a truly bad football team. The last time a Cowboys team looked so bad, Coach Tom Landry had hair. And on top of it all, an irritable, desperate New York Giants team was coming in promising a kick in the teeth Monday night.

The Cowboys took steps to ease those problems and perhaps even challenge for the playoffs by defeating the defending champion Giants, 33-24, before a shockingly supportive crowd of more than 55,000 in Texas Stadium. The victory raised the Cowboys' record to 4-3.

The defeat sent the Giants plummeting to 1-6 and the brink of elimination from a meaningful season in this strike-marred year.

But the Giants can stop moaning about what the replacement players did, because each Giants team now has lost three games. And the veteran Giants lost the latest one by committing four turnovers in the fourth quarter, allowing Dallas to score 19 points in the final 12 minutes to erase a 10-point deficit.

The offensive line let quarterbacks Phil Simms and Jeff Rutledge get sacked or disablingly socked seven times, by Ed (Too Tall) Jones and a bunch of aging, fading defensive linemen who rushed without the help of blitzes.

"They're a decent front four, but there's no way that should happen," guard Billy Ard said. "They're not the Bears, after all."

No, but they must have seemed as though they were to Simms, who was sacked five times and suffered sprained ligaments in his left knee that will keep him sidelined for one to four games.

Randy White said the defensive performance reminded him of "the old days," and Dorsett said it recalled years of the Doomsday defense. "We couldn't have won it without them," Dorsett said.

The game turned around with 10 minutes remaining when Jones tipped a pass by Simms that fell into the hands of Jim Jeffcoat, who ran 26 yards for the touchdown to tie the score, 24-24.

Roger Ruzek kicked one of his NFL-record-tying four field goals in the fourth quarter to give Dallas a 27-24 lead with four minutes to play, then another following a Giants fumble to make it 30-24 with three minutes to play.

The Giants had plenty of time, but Jones tipped another pass, this one falling in the chest of Randy White for an interception. Walker fumbled the possession away and New York had another shot. But Jones recorded his fourth sack on Rutledge and forced a fumble that Jeffcoat recovered.

When asked about making the playoffs, Giants Coach Bill Parcells said, "It'll be difficult now. We'll need some help, but things change in this league awfully fast. We'll see."

Center Bart Oates, the man who guaranteed victory for New York, said he would "get out of the predicting business."

While the Giants indulge in a day or two of self-pity and face up to the possibility of having to play out the string unless they win the remainder of their games, the Cowboys have a new outlook on their season.

Dorsett said the Cowboys decided during team meetings to "bury the hatchet and just play. The vibes were good and we fought like the dickens, even when it looked bleak. We were fed up with teams saying they're going to kick our butts. If you beat us, we're going to make you sore as hell."

Everson Walls said the Cowboys should be pardoned if they gloat a bit. "Here we were, trying to get our team back together internally, and teams are preying on us because we had people who crossed picket lines," he said. "It feels great that we turned back a bunch of guys that people thought were more determined than we were."

Whether the Cowboys can continue to play like this is another matter. Dallas only rushed for 26 yards, the lowest total in franchise history, and it would appear the 33-year-old Dorsett (14 carries for three yards) is about finished as a big-play, carry-the-load back.

Will the Cowboys play like the team that has defeated the Giants twice this season and five times in the last six meetings, or like the group that got shelled by the Eagles?

"This is a step in the right direction," Landry said. "I told the players it was our job to win the fans back. It wasn't the fans' job to come back to us."

For at least one evening, the Cowboys and their fans appeared to be back.