The Buccaneers (8-4) have won three of their last four games. Simms threw for 123 yards on 12-of-21 passing.
Cadillac Williams led the Bucs running attack with 96 yards on 22 carries.
Aaron Brooks passed for 215 yards with 18-of-34 completions, but was intercepted four times for the Saints (3-9), who have lost seven of their last eight games. Aaron Stecker made four catches for 55 yards in the loss.
Antowain Smith rushed for 49 yards on 18 attempts for New Orleans, which was playing the third of four games scheduled this season at LSU's Tiger Stadium.