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DENVER -- No gutsy 2-point call this week. Just a gut-wrenching close call.

Martin Gramatica's 43-yard field goal try with 1:55 remaining was wide right, and the Denver Broncos escaped with a 34-32 win over the New Orleans Saints on Sunday.

"It's nice to give up 32 points and still win the football game," Denver coach Mike Shanahan said. "That's the bottom line, you've got to find a way to win."

Thanks to Gramatica's dud, the charmed Broncos are 3-0 for the first time in five years despite allowing a whopping 28 points per game.

For the second straight week, the Broncos needed every ounce of offense they could muster, and for the second straight week they jumped out to a 21-3 lead only to be sweating it out at the end.

Last week, they converted a 2-pointer in the final seconds to beat San Diego 39-38.

This time, they denied the Saints (1-2) a 2-point conversion that would have tied it in the fourth quarter, then watched Gramatica's field goal attempt sail wide.

"We've got to be the luckiest team right now because of what's going on," Broncos cornerback Champ Bailey said. "We put ourselves in those situations, but right at the end things have been happening for us. You've got to take it as a good sign."

Gramatica declined to talk about his big miss, darting out of the locker room without even showering.

"The hold was good and he made good contact," holder Steve Weatherford said. "Other than that, I can't tell much more. He may have been making an adjustment for the one he missed at the end of the half."

One locker room over, the high-octane Broncos were kicking themselves, too.

"We're living on the edge," quarterback Jay Cutler said. "Offensively, we got the job done. We left a lot out there. I didn't play very well, missed some stuff, but defense stepped up when they had to."

Cutler wasn't as sharp as he was in his first two games, completing 21 of 34 passes for 262 yards and two TDs with one interception.

"Somebody's living right in that locker room," Cutler said. "We've got to straighten some stuff offensively and defensively. Special teams played well today, but we've got to tighten it up because we can't keep doing this. We're getting lucky at the end."

Brandon Marshall led the Broncos with six receptions for 155 yards and a touchdown but could have had 79 more yards and two more TDs if not for his less-than-fancy footwork: He stepped out of bounds at midfield on what would have been a third-quarter score, then failed to avoid a shoestring tackle on what would have been a game-clinching fourth-quarter TD.

The Saints never led, but they made a game of it after falling behind 21-3 early in the second quarter thanks to huge days by Drew Brees (39-of-48 for 421 yards and a touchdown) and Reggie Bush (178 all-purpose yards and two TDs).

Trailing 34-32 late in the fourth quarter, Brees and Bush got one more chance when cornerback Jason David scooped up Tony Scheffler's fumble at the New Orleans 5-yard line with 5:33 remaining.

The Saints reached the Broncos' 25-yard line and Gramatica, who was 8-for-8 as a member of the Saints before missing in the first half, barely missed this one to the right, as well.

The Broncos punted the ball back to the Saints in the waning seconds but Bush was corralled by Niko Koutouvides at the New Orleans 20-yard line with eight seconds left, and Brees was out of miracles.

Appropriately, his final play was a short toss to Bush, who caught 11 passes for 75 yards and a touchdown and rushed 18 times for 73 yards and a TD. He also returned two punts for 30 yards.

"This was a tough one to lose," Bush said. "We fought back and we just missed it. Barely."

The Saints pulled to 34-32 on Pierre Thomas' 10-yard TD run with 10 minutes left. The 2-point conversion, however, failed when Brees overthrew Bush in heavy traffic, one of several miscues that cost New Orleans a winnable game.

"What's hard about a game like this is there's a lot left on the field," Saints coach Sean Payton said.

Denver got a 34-yard fumble return for a touchdown from linebacker Nate Webster and took a 24-19 lead at the end of a wild first half in which the Broncos stuffed Thomas on fourth-and-inches in the waning seconds, only to see their offense hand the hard-earned momentum right back to the Saints.

Andre Hall was smothered by linemen Charles Grant and Sedrick Ellis for a safety. Brett Kern then punted the free kick out of bounds, giving the Saints the ball at midfield with 23 seconds left, but Gramatica's 51-yard field goal try was wide right as the crazy first half came to a close.

Game notes

The Broncos wore their alternate orange home jerseys for the first time since losing to Oakland 25-24 on Nov. 28, 2004. ... Saints CB Randall Gay (hamstring) and T Jammal Brown (groin) were injured.