ST. PETERSBURG, Fla. -- The hit total wasn't the key for the Toronto Blue Jays on Monday, because the Tampa Bay Rays finished with four more.

Toronto came through with men on base, stranding only four runners and making the most of its opportunities in an 8-5 victory over Tampa Bay on Monday night at Tropicana Field.

The Rays, coming home from an 8-2 road trip, pounded out 15 hits but stranded a season-high 14 runners and struck out a season-high 15 times.

"They had some chances. We got some big outs at key times with guys on base, but you've got to have that," Jays manager John Gibbons said. "They always put pressure on you. They really do. I can't remember scoring this many runs down here. I'm sure it's happened, but it doesn't happen too often."

Toronto broke open a 3-3 game with four runs in the sixth inning.

Designated hitter Jose Bautista got it started with a solo home run, his 15th of the season and the Jays' third solo shot of the game. Reliever Ronald Belisario replaced Tampa Bay starter Matt Andriese and struggled, giving up three hits in the inning.

Toronto (38-34) got an RBI double from left fielder Chris Colabello, an RBI single by right fielder Ezequiel Carrera and an RBI groundout by third baseman Danny Valencia.

Tampa Bay (40-32) cut its deficit to 7-5 in the seventh, starting with a solo home run by second baseman Logan Forsythe, his eighth homer of the season. Right fielder Steven Souza hit a triple off the left field wall, and with two outs, catcher Rene Rivera hit an RBI ground-rule double to the same corner.

Valencia's run-scoring single in the eighth made it 8-5.

The Rays loaded the bases with one out in bottom of the eighth, but Souza and shortstop Nick Franklin both struck out. Of Tampa Bay's 14 men left on base, nine were stranded in scoring position on inning-ending strikeouts by five different batters. It was only the third time this season that a major league team had 15-plus hits and lost in nine innings.

"We did a great job of getting guys on, but we didn't get those big hits with runners on second and third or bases loaded when we needed," said Rays outfielder Kevin Kiermeier, who went 3-for-6 but struck out to end the seventh.

Toronto's Drew Hutchison (7-1) allowed three runs on nine hits in five innings. Roberto Osuna threw two scoreless innings, striking out five, for his first save.

"Tip your hat to their guys making big pitches, especially the bullpen guys coming for them and doing a really good job," Kiermaier said. "They had a little more timely hitting than us, and a couple of solo home runs to give them a margin there. We didn't capitalize with runners on, and that will hurt you."

Andriese (2-2) gave up three home runs in his 5 1/3 innings after allowing three all season in a combined 50 1/3 innings between the majors and Triple-A Durham. He yielded four runs on five hits.

The Rays jumped out to a 3-1 lead through two innings.

Tampa Bay left fielder David DeJesus brought in the game's first run with a two-out, first-inning single up the middle. He drove in Kiermaier, who singled, stole second and advanced to third tagging up on a fly ball to center.

The Blue Jays answered in the second, tying the game when catcher Dioner Navarro, mired in a 1-for-16 slump, doubled and scored on a single by Colabello.

The Rays took the lead back in the second on Kiermaier's single that scored first baseman Jake Elmore, who walked, advanced on a bunt and took third on a wild pitch. Kiermaier scored on an single by third baseman Evan Longoria, but the Rays left the bases loaded when Forsythe struck out.

Toronto tied the game 3-3 on two solo home runs off Andriese -- shortstop Jose Reyes got his third in the third inning, and Navarro, facing his old team, hit his first of the season in the fourth.

"That was a good win for us," Gibbons said. "Hutch struggled a little early with his command, but he kicked it into gear. We got five out of him, which was huge. I can't say enough about Osuna, but he's been good all year, so that really doesn't surprise us."

NOTES: Tampa Bay LHP Matt Moore, who made his fourth rehab start Sunday as he returns from Tommy John surgery, will throw a bullpen session Tuesday. After that, the Rays will decide if he needs one more rehab appearance or if he can rejoin the rotation. ... Rays RHP Jake Odorizzi (oblique strain) and RHP Andrew Bellatti (shoulder) both threw full bullpen sessions, but there was no immediate word on what was next in their rehabs. ... The Blue Jays activated RHP R.A. Dickey from the bereavement list, recalled LHP Rob Rasmussen and selected the contract of RHP Todd Redmond. They had made three moves after Sunday's game, optioning LHP Phil Coke, RHP Scott Copeland and RHP Ryan Tepera to Triple-A Buffalo. Redmond allowed two runs in 1 2/3 innings Monday.