Bedard settled down, allowed three runs on six hits while striking out two in 4 1/3 innings. Of the 79 pitches he threw, 49 went for strikes.
"I think it was OK, just need to be more consistent with my off-speed and everything will be better after that," Bedard said. "... I think my cutter was better after the first inning. I'm just trying to get everything more consistent."
Blue Jays starter Sean Nolin found trouble in the bottom of the second. Justin Christian's sacrifice fly drove home the Rays' first run in advance of the big blow delivered by Mikie Mahtook, who homered with the bases loaded to put the Rays up, 5-2.
Nolin lasted just 1 2/3 innings, allowing five earned runs on five hits and three walks.
Evan Longoria's RBI single in the fourth off Chad Jenkins to put the Rays up, 6-3.
Up next: David Price will start Sunday afternoon, when the Rays host the Red Sox in a 1:05 p.m. ET contest at Charlotte Sports Park (live on MLB.TV). Price, who will be the Rays' Opening Day starter, will be making his third official start of the spring. Right-hander Allen Webster is scheduled to start for the Red Sox.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.