Brees finished with 363 yards on 23 passes for the Saints, who had won their season opener and then lost two games.
Two of the scoring tosses were to Lance Moore. Robert Meacham caught two passes for 99 yards, one of them a 47-yard touchdown.
Deuce McAllister ran for 73 yards and a touchdown in 20 carries for New Orleans.
The 49ers' J.T. O'Sullivan completed 18-of-36 passes for 257 yards and a touchdown, with two interceptions.
Arnaz Battle pulled in seven passes for 120 yards and Joe Nedney booted three field goals for San Francisco, also 2-2.