Craig Monroe also homered for the Tigers. Knotts (7-6) yielded one run, four hits and two walks.
Jorge Cantu doubled home the only run for the Devil Rays, who clinched fourth place with a victory in Friday's game to finish out of the AL East cellar for the first time since entering the league in 1998.
Tampa Bay needs a win on Sunday for its first 70-win season. Detroit needs a win to avoid 90 losses.
Thames became the 11th Detroit player with at least 10 home runs this season, a new major league record. The Tigers also reach the 200-homer mark for the seventh time in franchise history.
Tampa Bay starter Scott Kazmir (2-3) took the loss in six innings of work.