Myers drove in Evan Longoria, who also doubled off Rubby De La Rosa (0-1), to give the Rays a 4-3 lead.
Jake McGee (5-3) pitched a scoreless eighth before Fernando Rodney got three outs to earn his 34th save. The Rays lead the crowded race for the second AL wild card despite going 5-13 since Aug. 25.
David Ortiz and Jarrod Saltalamacchia homered for Boston, which has an 8 1/2-game lead over second-place Tampa Bay in the AL East.
The Red Sox threatened in the ninth when Stephen Drew had an infield single and pinch-hitter Mike Carp walked with one out. Rodney worked out of the jam when pinch-hitter Will Middlebrooks lined out to third and Dustin Pedroia popped out.
Ortiz has 43 career homers against Tampa Bay, the second-most by an opponent. Of those, 28 have come at Tropicana Field.
YANKEES 6, ORIOLES 5
BALTIMORE (AP) — New York's Brendan Ryan scored the tiebreaking run in the ninth inning on a wild pitch by Jim Johnson after the Yankees blew a four-run lead.
Mark Reynolds and Curtis Granderson homered for the Yankees, who remained one game behind Tampa Bay for the second AL wild card. New York travels next to first-place Boston for a weekend series.
New York led 5-1 before Nick Markakis hit a solo shot in the seventh and Danny Valencia homered with two on against David Robertson in the eighth.
But the Yankees bounced right back in the ninth with an unearned run against Johnson (3-8).
Mariano Rivera (6-2) got straight three outs in the bottom half and was given credit for the win by the official scorer because Robertson was ineffective in the eighth.
The start was delayed by rain for 1 hour, 18 minutes.
ATHLETICS 8, TWINS 2
MINNEAPOLIS (AP) — A.J. Griffin allowed two hits in seven innings for Oakland.
Josh Reddick homered and had three RBIs for Oakland, which has a 3 1/2-game lead over idle Texas in the AL West. It is Oakland's largest lead over the Rangers since Aug. 3. The teams are to scheduled play a three-game series this weekend in the Lone Star State.
Oswaldo Arcia homered for Minnesota, which has lost six of eight.
In winning his fourth straight start, Griffin (14-9) struck out eight and walked just one batter.
Making his first start since being recalled from Triple-A, Minnesota's Scott Diamond (5-11) allowed five runs — four earned — in 4 2-3 innings.
ANGELS 4, BLUE JAYS 3
TORONTO (AP) — Garrett Richards pitched 6 2-3 innings for his third straight win and Kole Calhoun hit a solo home run as Los Angeles completed a three-game sweep.
Erick Aybar had two hits and scored twice as the Angels won for the 15th time in 20 games and improved to 12-2 in their past 14 road contests.
Calhoun went 2 for 3 with a walk to help the Angels win for the 10th time in 13 meetings with the Blue Jays. Los Angeles recorded its first sweep in Toronto since April 16-18, 2010.
Jose Reyes homered and finished 4 for 4 with a walk, but the Blue Jays lost for the 29th time when scoring first.
Richards (7-6) allowed three runs and nine hits, walked one and struck out four. He's 3-0 with a 2.41 ERA in three September starts.
J.A. Happ (4-6) lost for the fourth time in five starts, allowing four runs and six hits in 4 1-3 innings.
INDIANS 14, WHITE SOX 3
CHICAGO (AP) — Ryan Raburn went 3 for 3 with a homer and five RBIs for Cleveland, which remained 1 1-2 games out of the second AL wild-card spot.
The Indians blew the game open with a seven-run, rain-delayed fifth inning, when their first nine batters reached base. Charlie Leesman, who relieved Chicago starter John Danks (4-13), faced seven Cleveland hitters, all of whom scored.
Nick Swisher had a solo homer and three RBIs, and Asdrubal Cabrera added a solo shot to support Corey Kluber (9-5), who gave up two runs and six hits in five innings.
Danks lasted four innings and allowed seven runs, nine hits and three walks in his third straight loss. In his last three outings, the left-hander has given up 17 runs in 14 1-3 innings.
Paul Konerko hit a solo homer for the White Sox, who are in last place in the AL Central and have lost 11 of 13.