Lance Moore and Drew Brees continued playing spectacular football for the New Orleans Saints Monday night.

But it was a run by Deuce McAllister that picked up the biggest cheers in a sold-out Superdome.

McAllister scored on a 3-yard third-quarter run, passing Dalton Hilliard to become New Orleans’ most-decorated scorer and the Saints beat Green Bay 51-29 in front of a national television audience.

Alex Brandon / Associated Press

Deuce McAllister waves to the fans after the Saints defeated the Green Bay Packers 51-29 Monday night.

Moore caught five passes for 115 yards and two touchdowns, while Brees was 20-of-26 for 323 yards and four touchdowns. Pierre Thomas added 87 yards and two scores on 15 carries.

McAllister had five yards on five carries and scored his 54th career touchdown as a Saint.

“The record is special,” McAllister said. “It’ll be something that someone else will come along and break. But as long as I hold it for a couple of days, I’ll be happy.”

Jason David picked off two passes and the defense held a potentially potent Packers offense to fewer than 400 total yards. Aaron Rodgers, Green Bay’s quarterback, was 23-of-40 for 248 yards and two scores, but he also threw three interceptions.

The win helped keep alive the club’s chances of sneaking into the postseason. New Orleans improved to 6-5, keeping pace with the rest of the NFC South. Carolina and Tampa Bay are 8-3 while Atlanta is 7-4.

It was New Orleans’ second win in a row, the first time that has happened since December 2007, and it was the first time the Saints played in the Dome since October.

“One thing we’ve talked about is pulling off five, six in a row,” McAllister said. “You had to get to two before you get to six.”

Added Brees, “It felt like things are clicking. We’ve all made the emphasis. We’re all in the middle of the pack. This is the time when teams separate themselves. We want to be one of those teams.”

Alex Brandon / Associated Press

Lance Moore (16) reaches for the end zone as the Packers' Aaron Rouse (37) hangs on in the first half Monday night.

The Saints’ onslaught began seconds before halftime when Garrett Hartley converted a 30-yard field goal with 2 seconds to go in the second quarter.

New Orleans got the ball to begin the third quarter and promptly drove 80 yards in 13 plays, eating 6:36 off the clock. The key play of the drive came when Thomas’ second and third effort on fourth-and-one picked up four yards.

Brees connected with Billy Miller for a 16-yard touchdown and a 31-21 lead with 8:34 to go in the third quarter.

Two plays later, David recorded his first interception of the night, bringing the ball back to the Packers’ 2 after picking up a key block by Scott Fujita.

“Jason did a good job of locating the ball and breaking on the ball,” Saints head coach Sean Payton said. “Those plays we made defensively in the second half made the difference in the game.”

Seconds later, McAllister took in his record-breaking touchdown, giving New Orleans a 38-21 lead.

After trading interceptions, New Orleans’ defense held the Packers to a three-and-out.

Again the Saints scored quickly, this time when Brees found Marques Colston on a stop-and-go route down the home sideline for a 70-yard touchdown.

With a little more than two minutes to go in the third quarter, New Orleans led 45-21.

“There was a flow to that game in the first half that both teams were moving the ball offensively,” Payton said. “The stop we came up with ended up being significant.”

The Packers cut into the lead early in the fourth when Rodgers hit Ruvell Martin for a four-yard touchdown before adding a 2-point conversion, but it was too little, too late.

Especially when Thomas wasn’t finished running. He reeled off a 31-yard touchdown run midway through the fourth. The 2-point conversion failed when McAllister was stopped short.

It didn’t start out so rosy for the Saints. Green Bay scored first, using a seven-play, 37-yard drive to take a 7-0 midway through the first quarter.

The Saints answered one play later. Brees found Moore open on a short slant route and the receiver did the rest, sprinting 70 yards for a game-tying touchdown.

Thomas put New Orleans up 14-7 on New Orleans’ next series with a 5-yard scoring run. The Packers tied it when Aaron Rodgers hit Greg Jennings for a 7-yard touchdown.

This time the Saints’ answer was a 14-yard Brees-to-Moore touchdown. And again the Packers came back, tying the game on Rodgers’ 10-yard touchdown run with 1:44 to go in the first half.

It was a Saints’ rout from there, giving them a two-game win streak heading into Sunday’s clash at Tampa Bay.

“It doesn’t become about a win streak as much as it becomes about playing another good football game and really trying to play a balanced game,” Payton said. “We thought we made some strides a week ago when we went and played Kansas City.”