Myers' sacrifice fly in the first inning put the Rays ahead to stay and his run-scoring single highlighted a three-run uprising in the third that handed a the Rays a 4-0 lead.
Desmond Jennings went 3-for-4 with two runs scored and Evan Longoria knocked in a run for the Rays, who entered the contest 2 1/2 games behind American League East-leading Boston.
Jeremy Hellickson (9-3) got the win, allowing two runs on five hits over five innings. He walked three and struck out three.
Toronto battled back with single runs in the third and fifth innings and mounted a challenge in the ninth against closer Fernando Rodney, scoring a run on Rodney's fielding error.
Rodney induced Adam Lind to fly out with runners on second and third, ending the game for his 23rd save.
Toronto's Mark Buerhle (5-7) took the loss, yielding four runs (three earned) on 10 hits over seven innings.
Jose Bautista hit his 22nd homer of the season for the Blue Jays.