With the game tied at 20 and 1:55 left, Bryant's third field, a 37-yarder, was a game-winner.
He had kicked two field goals in the second quarter, pulling Tampa Bay within 10-6 at halftime.
Quarterback Jeff Garcia completed only 9-of-23 passes for 119 yards, one touchdown and no interceptions, while Warrick Dunn gained 74 yards on 22 carries for the Buccaneers (9-3), who secured the win after defensive backs Jermaine Phillips and Philip Buchanon made key pass interceptions prior to Bryant's heroics.
New Orleans' Drew Brees, who faced a fierce pass rush, went 25-of-47 for 296 yards, two touchdowns and three interceptions.
Garrett Heartley kicked two field goals and Marques Colston caught six passes for 106 yards for the Saints (6-6), who fell three games behind Tampa Bay in the NFC South Division.