“You’ve got two teams that are pretty even,” Bear Bryant was fond of saying, “the team that makes the four or five big plays will win.” The Giants made more than just five big plays during the Monday Night Football game against Dallas, and more than that, they made most of them early. If it had been a boxing match, the Giants would have scored knockdowns in the first two rounds and then coasted to a unanimous decision.

The Giants were aided by an uncharacteristically bad decision from Bill Parcells, who spent most of the night wandering the sidelines looking as if he had been punched in the stomach. Down just 12–7 at the half, Parcells substituted the inexperienced Tony Romo for his longtime veteran Drew Bledsoe, which seemed to spread a signal of panic through the Cowboy offense. For all intents and purposes, this blew any chance the Cowboys had of mounting a comeback. Bledsoe hadn’t looked particularly good — he has managed to make a career out of winning most of the time without looking particularly good — but he was 7 of 12 for 111 yards while he was in the game. Romo, who spent the entire second half playing catch-up, was 14 of 25 for 227 yards with two relatively unimportant touchdowns and three very important interceptions.

Bledsoe’s one interception was important, too, but it wasn’t crushing. Sam Madison picked off a slant in the corner of the end zone to snuff a potential Dallas rally late in the second quarter. It wasn’t a terrible pass by Bledsoe; it was a terrible call by Parcells, who should have known better than to have his quarterback try to throw flat across the field from inside his opponent’s 10-yard line. Anyway, it was the Giants’ third big play of the first half, and it set the pace for the rest of the game.

In the course of the week, Tom Coughlin and the Giants’ offensive brain trust somehow figured out that scoring first might be a better game plan than waiting until they were down by two scores in the second half. They ordered Eli Manning to throw a long touchdown pass to Plaxico Burress, 50 yards to be exact, and, just like that, after five plays the Cowboys were back on their heels. Later in the first quarter, LaVar Arrington sacked Bledsoe for a safety to make it 9–0, and then came Madison, and the Giants never looked back. Tiki Barber, having lulled the Cowboys into a false sense of security by announcing his retirement earlier in the week, rushed for 114 yards and ran down the clock on the Cowboys’ offense for this game, and, most likely, for their season.

After the euphoria of a big Monday night win over Parcells and the Cowboys on their home field had died down, the Giants still have more to celebrate than to worry about — but it’s close. The Giants have won their last three games and outscored their opponents by 23 points. The biggest single factor in the turnaround has been the emergence of the pass rush, or, specifically, the emergence of pass rushers besides Michael Strahan, most notably Osi Umenyiora on the other end of the defensive line. Freed from brutal double blocking, Strahan has gone savage in the last two weeks, playing his best football in nearly two years.

Everyone else on the defense has played well, too, though the downfield coverage has looked better than it is because of the limited time the pass rush has allowed opposing quarterbacks. There was nothing wrong with Drew Bledsoe Monday night that having three more seconds to throw the ball wouldn’t have cured, but the Giants wouldn’t give it to him.

The second best thing about the Giants on Monday night was the absence of penalties — just three, their lowest total of the season (though once again, they drew more than their opponents with just a single flag being thrown on the Cowboys).

There were, however, some potentially big downsides. After the touchdown pass on the first possession, Manning was wildly inconsistent against a disorganized and demoralized Cowboys defense. In the first five minutes of the game, he was just 10 of 25 for 129 yards with an interception. To his credit, he chose to eat the ball twice on sacks rather than put a ball up for grabs that might have given Dallas a chance to get back in the game. But it’s disturbing that after demonstrating the ability to strike early, the Giants couldn’t have come up with a short, controlled passing game to complement Barber’s inside slashes.

More ominous is the loss of Arrington for the season with an injury to his left Achilles tendon, an injury that down the stretch may prove more significant than a victory in this game.

The Giants now have two relatively easy games at home against Tampa Bay and Houston to work in a replacement and work out the offensive kinks before facing the league’s best team, the Bears, at the Meadowlands on November 12. More than likely, the Giants are the second best team in the conference, a case they will have to make in the next two games before taking on the Bears. If they continue their newfound propensity for making big plays – and for not drawing flags — there’s every reason to expect that the meeting with Chicago will be a preview of the NFC championship game.

Mr. Barra is the author of “The Last Coach: A Life of Paul ‘Bear’ Bryant.”