ST. PETERSBURG, Fla. -- Toronto designated hitter Kendrys Morales went into the Thursday game with just a .125 average and one RBI, but manager John Gibbons wasn't surprised at all that he hit a grand slam to power the Blue Jays to a 5-2 win over the Tampa Bay Rays at Tropicana Field.

"It was just a matter of time before the guy started heating up," said Gibbons, remembering a grand slam Morales hit last season while with the Kansas City Royals against his Blue Jays. "He was barreling everything. He doesn't have much to show for it, but I think he's locked in. He's had balls go to the track, and when the summer heats up, those balls are home runs. He could easily be hitting .500 right now."

Toronto (1-2) bounced back after two opening losses at Baltimore. The Rays (2-2) struggled on offense, falling behind 5-0 before scoring in the seventh inning.

Jays starter Marcus Stroman (1-0) struck out five while allowing one run on six hits and two walks in 6 1/3 innings.

"I thought the pitcher was very good, a really good, solid outing," Gibbons said. "They struck some hits off him late, but (Joe) Biagini came in and shut them down (in the seventh)."

Rays starter Blake Snell (0-1) held Toronto to four hits in 6 2/3 innings, but one of them was Morales' slam. Toronto added a fifth run of Snell in the seventh on Darwin Barney's bunt single, scoring Russell Martin, who had reached base on Snell's fifth walk. Three of those walked batters wound up scoring for Toronto.

"Upset about the walks, but felt good, felt I was competing," Snell said. "Walks, I felt like that's always the thing that gets me. I have to attack and do some things mentally to stay into it."

Tampa Bay hit into four double plays and had an out at the plate. The Rays finally strung together three singles in the seventh and scored on Logan Morrison's RBI single to right field, chasing Stroman from the game.

Toronto backed into a save situation, as reliever Joe Smith gave up a walk and a double in the ninth, and Jason Grilli came in and allowed Brad Miller to score on a wild pitch.

Grilli got the final two outs on strikeouts for his first save of the season.

Each team had only two hits in the first five innings, but Toronto had much more to show for it, thanks to Morales' two-out grand slam in the third inning.

Barney, batting ninth, hit a one-out single in the third, and with two outs, Snell walked Josh Donaldson and Jose Bautista to load the bases for Morales, who crushed an 0-1 pitch to left-center for a 4-0 lead.

"Things I can fix, things I'm aware of so I can get better," Snell said of his five walks, which matched a career high.

Toronto had scored only three runs total in its first two games of the season, both losses at Baltimore, before getting four runs on one swing.

Tampa Bay's Steven Souza Jr. doubled to lead off the fifth and advanced on a groundout, but Stroman threw home on a comebacker by Tim Beckham, and catcher Martin tagged out Souza. The Rays challenged the call, checking if Martin violated the collision rule, but the call was upheld.

NOTES: C Luke Maile, designated for assignment by the Rays on Sunday, was claimed by the Blue Jays on Thursday and will report to Triple-A Buffalo. ... Rays OF Colby Rasmus, on the disabled list as he recovers from hip surgery last fall, began a rehab assignment with Class-A Charlotte on Thursday. Rasmus went 0-for-3 with an RBI groundout. ... Rays RHP Brad Boxberger, on the disabled list with a right flexor strain, isn't expected back until at least May as he's dealing with an elbow injury as well and still must essentially go through an entire spring training before he joins the team, the Tampa Bay Times reported. ... Toronto's three runs in the first two games of the season matched the second-fewest in franchise history, behind only the 1985 Blue Jays, who scored two in their first two games. ... C Jesus Sucre made his Rays debut, going 0-for-3 out of the No. 9 hole in the lineup. Derek Norris played the first three games at catcher.