Mark Buehrle made his second start of the spring, and the Blue Jays veteran held the Rays scoreless through 3 1/3 innings, allowing two hits and striking out two.
Rays Opening Day starter Alex Cobb made his second start of the spring and cruised through the first before finding trouble in the second.
Caleb Gindl doubled to left to lead off the inning, and Justin Smoak followed with a single. One out later, Devon Travis stroked an RBI single to left for a 1-0 Blue Jays lead.
The Blue Jays added two more in the third on a one-out single by Josh Donaldson.
Cobb allowed three earned runs on five hits and a walk while striking out four in 2 1/3 innings.
"You can either hang your head and walk out the door and be upset about it," Cobb said. "Or you can find some positives out of it and try to use that to make yourself better and grow for the season. By no means am I doubting myself. There was some good stuff that happened that I can learn from."
The Rays scored two more runs in the eighth inning to bring the score to 10-3 when Nick Franklin singled to Chris Colabello, who committed a fielding error.
Up Next: Chris Archer will make his third start of the spring when the Rays travel to Clearwater to play the Phillies Friday afternoon in a 1:05 p.m. ET contest airing on MLB.TV. The Rays right-hander is working on his changeup and a quicker delivery to the plate with runners aboard. Also expected to see action are Jim Miller, Mike Montgomery, Everett Teaford and Grayson Garvin. Joely Rodriguez will start for the Phillies.
Bill Chastain is the Rays beat reporter for MLB.com. He has been covering the club since 2004.
This story was not subject to the approval of Major League Baseball or its clubs.