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.
Aaron Carter is still in love with Hilary Duff
Millions of Getty images now available for free via embed tool