Did anyone notice that the Giants have the best offense in the National Football League? Not their coach, apparently, who still seems to think his team is going to win on defense and keeps reining his horses in until the game is on the line and he has no choice but to turn them loose … But more of that in a minute.

If Eli Manning’s first big step forward was the Giants’ Week 3 loss in San Diego, yesterday’s thriller over Denver was a leap. For the first time this season, the Giants beat a team better than they are and won a game they should have lost – something you sort of have to do a couple of times a year if you want to be a serious playoff contender.

Kept in check throughout most of the game by a combination of Denver’s bewildering blitzes and coach Tom Coughlin’s inexplicable conservatism, the Giants found themselves down 23-10 in the fourth quarter and their season perilously close to a crash-and-burn. With no other choice, Coughlin gave Eli the green light and all of a sudden, there’s hope.

More than hope, really – there’s promise. The Giants have the best young passer in the league (which Manning can safely be called right now), one of the most dangerous wideouts in Plaxico Burress, a mother of a tight end in Jeremy Shockey, a terrific and versatile running back in Tiki Barber, and, though they themselves had forgotten it until their last play of yesterday’s game, an efficient and reliable second wideout in Amani Toomer. (How is it possible that a man approaching 500 career catches could have just two for touchdowns in his last 22 games?)

The Giants offense is consistently dangerous and dangerously inconsistent; it is also the leading scoring unit in the NFL at 28.8 points per game. For the first half against Denver, they seemed out to prove how many unforced errors they could make and still stay in the game. For instance, in the second quarter, Burress, badly beating the Broncos superb corner, Champ Bailey, took in a 60-yard touchdown pass from Manning only to have it called back on offensive pass interference. (The call was dubious, but Plaxico should have been keeping his hands to himself.)

That was merely the most spectacular of the Giants offensive goofs, which included eight penalty flags, six of them assessed. (The defense drew just one, though the linebackers and defensive backfield combined to drop four balls that could have been intercepted.)

Down by six points with five minutes to play, the Giants managed to discover yet another way of playing brinkmanship. From their 40, Manning flipped a short pass to Shockey, who took it for eight yards only to find the Giants had lined up in an illegal formation. How a team playing in front of friendly fans in its sixth game of the year doesn’t know how to lineup properly is baffling. In any event, instead of second-and-2, the Giants had second-and-15, the kind of situation in which disasters occur, and one did when Bailey, for once correctly anticipating one of Eli’s passes, jumped in front of Burress and made a diving interception. It was just the fourth pick of the year for Manning, which is amazing considering how much catch-up he’s had to play.

But the Giants defense, playing perhaps its best ball of the year, forced a punt, giving Eli a chance to launch his legend. The final drive was the stuff of high drama, but it might not have been necessary had the Giants not been playing in a fog for so much of the afternoon. This included the brain trust on the sideline, which failed time and again to solve the Bronco blitz, though Eli’s agility prevented sacks. (He was hit or knocked down seven times.)

Denver regularly put seven and sometimes eight men on the line of scrimmage, but none of the Giants’ coaches could ever seem spot their uncovered receivers. For most of the game, Manning stared across the field in bewilderment at his coaches, looking like a kid in a school play in need of a line. Even while pulling off the mini-miracle in the final seconds, he seemed uncertain of what his bosses wanted him to do.

Down 23-17 with 17 seconds and a timeout left, Coughlin made a curious call: a screen pass over the middle to Barber. Curious not only because it not only required Manning to deliver the ball into a crowd, but because it was designed to hit the intended receiver short of the goal line. Barber was tackled at the two with nine seconds to play as tens of thousands of amateur coaches screamed Timeout! Timeout! Eli had to wait for a nod from Coughlin before informing the ref.

One wonders what possible alternative he could have thought there was to a timeout in that situation, and why he felt it necessary to waste a couple of precious seconds waiting for Coughlin’s okay.

This coming Sunday, the Giants play another home game against one of their two Eastern rivals tied for first place with a 4-2 record. The game will pit the NFC’s – and probably the league’s – best offense against one of the conference’s best defensive units, one considerably better than either Dallas’s or Denver’s – Joe Gibbs’s Washington Redskins. It’s time for Tom Coughlin to take the leash off and let slip his dogs of war.

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