Brees finished with 267 yards and three TDs. After rushing for 140 yards or more in each of its previous three games, New Orleans (5-6) managed only 59 yards against San Francisco (8-2-1).
One of Brees' scoring passes went to Marques Colston, who set a Saints record with his 56th career touchdown with the club.
The Niners gained 144 yards on the ground, led by Gore with 83. The Saints shut down tight end Vernon Davis, the player they feared perhaps the most, but the Niners' other tight end, Delanie Walker, had three catches for 81 yards, including one for 45 yards to set up a touchdown.
San Francisco's interceptions turned a 14-7 deficit into a 28-14 lead.
Brooks snagged the first, returning it 50 yards late in the first half. The second came on Brees' first pass of the second half. The ball deflected off Colston's hands as the leaping receiver was upended and briefly shaken up. Whitner snagged the deflected pass and returned it 42 yards to make it 28-14
Since losing to the New York Giants on Oct. 14, the Niners are 5-0-1 and now hold a 2 1/2-game lead in the NFC West with five games to go.
It seems their biggest problem at this point is deciding who should be their No. 1 QB. Smith, who led the Niners to the NFC title game last season, started the first nine games this season before his injury.
The Saints, meanwhile, missed a chance to pull into a tie for the last NFC wild card berth, and remain a game out with another tough game coming up at Atlanta on Thursday night.
Kaepernick used the running ability that served him so well in college at Nevada to give the Niners the early lead, scoring on a read-option run that fooled the Saints defense as well as the Superdome crowd, which erupted, initially believing the play had been snuffed out, while Kaepernick scampered to his left and scored easily.
The drive was highlighted by Mario Manningham's 40-yard gain after Kaepernick found him wide open on a short crossing route.
Then, New Orleans' offense, which could not muster a first down on its first two drives, suddenly ignited, marching 79 yards in 10 plays highlighted by Joe Morgan's diving 33-yard catch to tie it on tight end David Thomas' 6-yard catch.
San Francisco entered the game allowing a league-low 13.4 points per game. The Saints surpassed that in the second quarter when Brees hit Colston to make it 14-7 and capitalize on Ted Ginn Jr.'s fumbled punt, which Rafael Bush had recovered on the 49ers 10.
New Orleans looking intent on going up by two scores after Kaepernick's first career interception on an underthrown pass that cornerback Patrick Robinson easily caught. But the crowd has hardly finished celebrating when Brooks stepped in front of Brees' pass for Jimmy Graham and returned it 50 yards to tie it at 14 shortly before halftime.
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San Francisco 31, New Orleans 21
San Francisco 7 7 14 3 31
New Orleans 7 7 7 0 21
SF • Kaepernick 7 run (Akers kick), 7:21.
NO • D.Thomas 6 pass from Brees (Hartley kick), 1:45.
NO • Colston 10 pass from Brees (Hartley kick), 7:53.
SF • Brooks 50 interception return (Akers kick), :22.
SF • Gore 6 pass from Kaepernick (Akers kick), 12:17.
SF • Whitner 42 interception return (Akers kick), 11:30.
NO • Collins 2 pass from Brees (Hartley kick), 7:19.
SF • FG Akers 27, 7:50.
Attendance • 73,147.
First downs 18 19
Total Net Yards 375 290
Rushes-yards 31-144 21-59
Passing 231 231
Punt Returns 2-13 1-3
Kickoff Returns 1-23 5-148
Interceptions Ret. 2-92 1-0
Comp-Att-Int 16-25-1 26-41-2
Sacked-Yards Lost 0-0 5-36
Punts 4-46.8 5-50.4
Fumbles-Lost 1-1 0-0
Penalties-yards 10-68 4-53
Time of Possession 30:06 29:54
Rushing • San Francisco, Gore 19-83, Hunter 4-28, Kaepernick 6-27, Dixon 1-5, Jacobs 1-1. New Orleans, Ivory 8-34, Ingram 10-27, P.Thomas 1-0, Brees 2-(minus 2).
Passing • San Francisco, Kaepernick 16-25-1-231. New Orleans, Brees 26-41-2-267.
Receiving • San Francisco, Manningham 5-69, Walker 3-81, Miller 3-37, Crabtree 3-26, Gore 2-18. New Orleans, Sproles 7-65, Colston 4-36, Graham 4-33, D.Thomas 4-24, Moore 3-61, Collins 2-9, Morgan 1-33, Henderson 1-6.
Missed Field Goals • San Francisco, Akers 50 (WL), 33 (BK).