Kaepernick -- starting a second straight game in place of the concussed Alex Smith -- completed 16-of-25 passes for 231 yards with a TD pass and an interception, while also rushing for 27 yards with a score on six carries.
Frank Gore ran the ball 19 times for 83 yards as the 49ers (8-2-1) logged their second straight win.
The 49ers' Donte Whitner and Ahmad Brooks helped out on defense with interception returns for touchdowns.
The Saints (5-6), meanwhile, saw their three-game winning streak snapped despite three TDs and 267 passing yards from Drew Brees.
The New Orleans quarterback also surrendered the two interceptions, however, and was sacked five times.