The Rays maintained their lead in the crowded chase for the second wild card berth in the American League while the Red Sox failed in their bid to become the first team in the majors to win 90 games this season.
Boston rallied into a 3-3 tie in the sixth on a solo homer by Davis Ortiz and an RBI double by Stephen Drew, but the Rays regained the advantage against Jose De La Torre (0-1) in the eighth.
Evan Longoria reached on a one-out double in that inning and, with two away, Myers doubled to right to bring in the go-ahead run.
That allowed Tampa Bay to salvage the finale of a three-game series and win for only the second time in seven games.
Jake McGee (5-3) struck out two in the eighth, his only inning of work, to get the win. Fernando Rodney put two runners on in the ninth before collecting his 34th save.