The Buccaneers were without starting quarterback Josh Freeman for most of the game. He fractured his right thumb early in the first quarter after completing 2-of-4 passes for 21 yards.
Freeman was followed by Josh Johnson, who was 6-for-10 for 113 yards before giving way to Carpenter.
Carpenter went on to complete 8-of-11 passes for 79 yards, including a 5-yard scoring toss to Terrence Nunn with less than 6 minutes to go.
Kareem Huggins ran eight times for 44 yards for the Bucs, now 1-1. Connor Barth hit two field goals for the winners.
Matt Cassel went 14-of-19 for 125 yards and a touchdown for the 0-2 Chiefs. Jackie Battle 59 yards on 11 carries.