Justin Griffith scored a touchdown and gained 57 yards on 12 carries for the Falcons, who have won two in a row following a four-game losing streak.
Dunn limped off the field with a left calf injury, while Norwood injured his right knee.
Bruce Gradkowski was 13-for-24 for 121 yards for Tampa Bay. Tim Rattay was 9-for-13 for 83 yards, and Matt Bryant kicked two first-half field goals for the Buccaneers (3-10), who have a three-game losing streak.
Tampa Bay lost two fumbles and has 14 turnovers in its last five games.
Celebrity Families of 2014 [PHOTOS]