TORONTO -- By trying not to do too much, Brandon Morrow ended up with his best start of the season.
Morrow, who didn't allow his first hit until there were two outs in the sixth, said he succeeded by taking a little off his pitches.
"I've had better stuff, meaning a nastier slider or a better fastball," Morrow said. "But I think this is probably my best game in terms of making pitches, not trying to throw that nasty curveball and instead just flipping it in for a strike."
Rays manager Joe Maddon, whose team has lost six of eight, noticed the difference in Morrow.
"He was a little bit softer than normal," Maddon said. "It looked like he was trying to tone it down a bit to throw more strikes. He pitched fine. He didn't have, for me, no-hit stuff going into the sixth inning. We just weren't very fortunate to that point."
Maddon said he did not want to make Jaso bunt, so he sent Longoria to make sure Toronto, playing with the infield in, could not turn a game-ending double play.
Gabe Kapler ended it by grounding into a fielder's choice, giving Gregg his 14th save in 16 chances.
Adam Lind hit a two-run home run for Toronto.
Morrow (4-4) left to a standing ovation when he was replaced after Jaso's leadoff single in the eighth. He gave up one run and three hits, walked two and struck out one.
"My last five outings, the times I've backed off a little and really focussed on keeping the ball down, keeping it to the corners, I've pitched better," Morrow said. "I've calmed myself down and relaxed and made my pitches instead of overthrowing and trying to strike everybody out."
Rodriguez ended Morrow's no-hit effort with an infield single, touching the base just before Lyle Overbay caught a bouncing throw from shortstop Alex Gonzalez. Rodriguez was picked off by catcher Jose Molina.
Morrow issued leadoff walks to Upton in the third and Pena in the fifth, but got double plays both times, spearing a hard comebacker from Jaso to start a 1-6-3 double play in the fifth.
"It was one of those nights where things were falling for them and things weren't falling for us," Jaso said. "We hit a lot of balls hard throughout the game."
Zobrist singled up the middle to begin the seventh but was erased on Carl Crawford's fielder's choice. After Longoria flied out, Pena launched a drive to deep center that Vernon Wells hauled in with a leaping catch up against the wall.
"If that ball went over the fence, that's a whole different ball game right there," Jaso said.
Lind hit a two-run homer to left off Matt Garza (5-4) in the first, his eighth, and first since May 21.
"He hit a good pitch," Garza said. "It was a fastball down and away and he just went and got it."
The Blue Jays, who lead the major leagues with 89 home runs, finished May with a club-record 54 homers. That's the most by any team in a single month since Atlanta hit 55 in May 2003. The major-league record for home runs in a month is 58, set by Baltimore in May 1987 and matched by Seattle in May 1999.
"They beat us with the home run," Maddon said. That's their game."
Garza came in 5-3 with a 2.19 ERA in 11 previous starts against Toronto but has lost to the Blue Jays twice this season. The right-hander, winless in five starts, allowed three runs and a season-high 10 hits in 6 1/3 innings. He walked two and struck out three.
"It's a lot of what you saw last year where we didn't score enough runs for him and, all of a sudden, his record isn't what people would expect of him," Maddon said. "He got off to a great start, wins-wise. We just haven't scored him enough runs lately."
Garza gave up five runs and eight hits in five innings of a 6-5 home loss to the Blue Jays on April 23.
Toronto optioned RHP Josh Roenicke to Triple-A Las Vegas after the game, clearing a spot for LHP Brian Tallet, who will come off the 15-day DL to start Tuesday. ... Rays C Kelly Shoppach, out since April 11 following right knee surgery, went 1 for 3 with a two-run single in the first game of his rehab assignment at Triple-A Durham. ... Rays SS Jason Bartlett (right hamstring) missed his second straight game and will not start in this series, Maddon said. If he improves, Bartlett could come off the bench. ... Tampa Bay OF Matt Joyce (right elbow) returned from his rehab assignment and was optioned to Triple-A. ... Toronto OF Travis Snider, out since May 15 with a sore right wrist, has resumed swinging but has not begun hitting, manager Cito Gaston said. ... Attendance was 11,335.