ST. PETERSBURG, Fla. -- In a chaotic game -- a fan caught a ball ruled a double, then overturned to a Blue Jays home run, and another complicated challenge caused a five-minute delay, immediately before a two-run Jays home run -- the Blue Jays got enough clutch outs to escape with a 5-3 win over the Tampa Bay Rays on Monday at Tropicana Field.

Toronto (2-0) got home runs from Josh Thole, Michael Saunders and Josh Donaldson, building a 5-1 lead that was threatened in nearly every inning, stranding six runners in scoring position. R.A. Dickey (1-0) lasted five innings, with four relievers combining to close out the Rays (0-2).

Rays starter Drew Smyly was upset about both home runs, first the fan-aided Josh Thole solo shot, then the long delay that preceded Michael Saunders' two-run shot.

"I'm not going to make excuses," Smyly said. "It is a little ridiculous that they spend 5-10 minutes on replay. I don't agree with that. And from all our angles, we don't know how you can overturn Thole's home run as well. It is what it is and we got beat 5-3."

Tampa Bay had the tying run on base in the sixth and eighth innings, but Jesse Chavez struck out two batters to end the sixth and Drew Storen struck out pinch-hitter Hank Conger to end the eighth. Roberto Osuna, who got the save in Sunday's opener, got a 1-2-3 ninth on seven pitches for a second save.

"They were great," manager John Gibbons said of his bullpen. "Everybody had a good spring, a little of a pleasant surprise but you never know until you see them out there."

The Rays' influx of new hitters couldn't get the job done Monday, with five newcomers going a combined 0-for-12 on the night. Kevin Kiermaier went 3-for-3 with a walk for the Rays, who could only bring him in one of the four times he reached base.

Toronto jumped out to a 5-1 lead after five innings, getting almost all their runs on three home runs off Smyly, who didn't allow a hit until the third. The first home run was a bit of controversy -- a Rays fan in right-center field reached down across the yellow line that marks a home run to catch a ball hit by Thole. The ball was initially ruled a double by fan interference, but after a review, it was determined to be a home run, tying the game at 1-1.

The Blue Jays added a run in the fourth on a sacrifice fly by Troy Tulowitzki, then endured a lengthy replay on a ball caught at the foul line in deep right field that later popped out of the glove of Rays right fielder Steven Souza.

There were differing accounts of what was called and challenged, but the Rays said it was initially ruled a fair ball, dropped and thrown to first base for an out; then overturned to a completed catch in foul territory.

Immediately after the delay, Toronto got a two-run shot from Saunders, and another in the fifth on Donaldson's first home run of the season for a 5-1 lead. Donaldson came into the night 5-for-8 all-time against Smyly with a home run.

"It doesn't help," Rays manager Kevin Cash said of the delay. "Commotion, confusion there, but any time with any pitcher, you don't want to take them out of any rhythm at all."

The Rays, who led 1-0 on Souza's solo home run in the second, got another run by in the fifth, largely on the hustle of Kiermaier. Kiermaier led off the inning with a single, sped to third on a single up the middle by Curt Casali, and then scored on a wild pitch, just beating the throw back home to Dickey.

The Rays consistently weren't able to capitalize on opportunities -- runners at second and third with one out in the first, at second with one out in the second, and first and second with no outs in the fifth, each time coming up empty.

Toronto center fielder Kevin Pillar made a wild catch to save a double in the seventh, catching a fly ball at full extension then crashing head first into the wall, needing a moment before he was back on his feet.

"Kevin got into pro baseball playing the game one way and that's not going to change," Gibbons said. "That's how you win games. You've got to take away hits."

NOTES: Both teams kept nearly the same batting order from Sunday's opener, save a change at catcher for both teams, with Curt Casali behind the plate for the Rays and Josh Thole catching for Toronto. ... Jays reliever Roberto Osuna, 21, got the save in Sunday's opener, becoming the youngest player in history to record a save on Opening Day. ... Rays starter Chris Archer, who took the loss in Sunday's opener, became the first pitcher since the Cards' Bob Gibson in 1975 to strike out at least 12 in a season opener and still lose. Archer was also just the fourth pitcher since 1900 to have at least 12 strikeouts in an outing of five innings or less -- the Rays' Alex Cobb is one of the others, from a 2013 game.