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: Right-hander Todd Redmond will take the mound when the Blue Jays host the Orioles on Sunday afternoon at 1:05 p.m. ET at Florida Auto Exchange Stadium. Redmond is tentatively scheduled to throw five innings as he continues to compete for the final spot in the rotation. Top prospect Aaron Sanchez and right-hander Dustin McGowan also are scheduled to pitch for the Blue Jays. Following a day off to avoid a long drive to Port Charlotte, Fla., the majority of Toronto's starting lineup is expected to return, including the likes of Jose Bautista, Edwin Encarnacion and Melky Cabrera.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.