So it figured to be close and rousing Monday night, and it was.
The Giants, leading by 10 points at the start of the fourth quarter, gave it away in the last 14 minutes as Dallas intercepted two passes and recovered two fumbles--all in good field position--to win easily, 33- 24.
"It turned into a nightmare late in the game," said Bill Parcells, the coach who led the Giants to the Super Bowl championship last winter.
"They always self-destruct against us," Dallas cornerback Everson Walls said after the Giants lost first their cool and then the game in the wild final minutes.
Quarterback Phil Simms, whose long touchdown passes to wide receiver Lionel Manuel had moved the Giants into a 24-14 lead on the first play of the fourth quarter, injured his left knee when sacked by Cowboy end Jim Jeffcoat on one of the interceptions that soon followed, and went off on a stretcher.
It was a ligament injury but not serious, the doctors said. Simms will be out a week or two.
The game's turning point was Dallas' first interception of the fourth quarter, which Simms threw when the Giants were leading, 24-17, five minutes into the final period.
Dallas defensive lineman Too Tall Jones deflected the ball to Jeffcoat, who ran 26 yards for the game-tying touchdown.
"We were making the big plays when we needed them," Cowboy Coach Tom Landry said. "Momentum is a major thing in football, and we got the turnovers in the fourth quarter that kept it going."
When the Giants gave the ball away almost every time they saw it, the Cowboys scored 19 points in the last 14 minutes as a new Dallas specialist, Roger Ruzek, kicked a National Football League record-tying four field goals in one quarter.
This came as no surprise to the football fans who have watched this rivalry over the years. The Cowboys, who hold 35-14-2 advantage, are 5-1 in their last 6 meetings and 11-1 in the last 12 at Texas Stadium.
Compounding their problems in this game, the Giants curiously kept trying to run the ball against a Dallas team whose weakness is pass defense.
Though he threw only 8 times in the first half and only 13 times thereafter, Simms led the Giants 80, 70 and 34 yards to their three touchdowns.
The bombs to Manuel were 50 and 33 yards.
"(Manuel) beat (cornerback Ron) Francis on single coverage," Landry said.
The Cowboys, on the other hand, had some good fortune on every touchdown and field goal they made, getting a 19-yard interference penalty and a fumble recovery at the New York 18-yard line ahead of their first two touchdowns in the 14-10 first half.
Thereafter, they got even luckier in the strangest fourth quarter of the year to improve their NFL record to 4-3.
The Giants fell to 1-6, due partially to strong performances by Dallas quarterback Danny White and fullback Herschel Walker, but due mainly to the defensive play of Jeffcoat and Jones and the good fortune the Cowboys always seem to have in Giant games.
The Cowboys got three of their six sacks and both interceptions in the fourth quarter, along with the two fumbles. Setting some kind of record, a Dallas lineman, Randy White, and two linebackers, Mike Hegman of Dallas and Lawrence Taylor of New York, made all the interceptions.
It was Taylor's play that moved the Giants close enough to score the field goal that made them seem to be an easy 10-point winner in the fourth quarter.
The Cowboys, in a game in which they produced three touchdowns and four field goals, marched 18 and 0 yards to two of their touchdowns and 16, 7 and 0 yards to three field goals.
They didn't, in other words, do very much in the opinion Stephen Baker, the Giants' fast rookie receiver, who noted that both of the late interceptions came on tipped passes.
How lucky was it? This was the first time in more than a year that the Cowboys have won on their home field.
But conceivably, it turned their season. With some new players and a slightly different design, the Cowboys have been struggling. Maybe they needed one like this.