Tampa Bay remained 2 1/2 games in front of the New York Yankees for the second American League wild card berth. Cleveland finished the night 3 1/2 games back.
Jeremy Hellickson threw 5 1/3 shutout innings and four relievers combined to hold the Angels to a run on three hits.
Myers hit a solo homer in the second and launched another blast in the seventh after Desmond Jennings had drawn a one-out walk.
The Angels' only run came on a seventh-inning home run by Chris Iannetta.
Hellickson (11-8) allowed four hits and walked two to get the win. Fernando Rodney struck out two during a perfect ninth and collected his 32nd save.
Jered Weaver (9-8) allowed both of Myers' home runs and four other hits over seven innings to take the loss.