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 came during a 21-0 spurt that gave the Niners 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.
Brooks, Aldon Smith and Justin Smith each had 1 1/2 sacks, all in the second half.
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. The Saints, meanwhile, missed a chance to pull into a tie for the last NFC wild card berth, and remain a game out.
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.