The Rays snapped a three-game losing streak, taking control with a three-run fourth and then coasting behind a solid pitching performance from their starter and bull pen.
Rodney bounced back from a blown save on Tuesday in which he let a one-run lead get away in the ninth against the Angels.
Matt Joyce put Tampa Bay in front with a sacrifice fly in the first and the Rays then broke through with a big inning in the fourth.
After putting runners on second and third with one out, Desmond Jennings scored in the fourth on an infield single by David DeJesus. A base hit by Ben Zobrist brought home another run and Tampa Bay scored again when shortstop Erick Aybar committed a throwing error on Evan Longoria's grounder.
Garrett Richards (5-6) was charged with the loss, surrendering four runs on seven hits in 3 1/3 innings.