Bedard gave up one hit in seven scoreless innings and the Rays had 10 hits in a 7-1 victory Saturday over the Cleveland Indians that broke a four-game skid.
Winning his second straight start after 15 without a win, Bedard gave up a double to Ryan Raburn in the second inning, Cleveland's only hit until Lonnie Chisenhall led off the ninth with a single off Grant Balfour.
Just as refreshing for the Rays, who had lost six straight home games, was the offensive output led by James Loney, who had three hits and drove in two runs. The Rays had only 10 runs while losing the four preceding games on their homestand.
"Tonight we came out ready to swing and it led to good things," said Matt Joyce, who drove in two runs with sacrifice flies. "We have some great players here. Obviously, this year hasn't gone the way we wanted so far and it was a rough week for us, but we've still got a little ways to go."
Bedard (2-1) is the only Rays starter to go six innings over the team's last seven games. Manager Joe Maddon "was tinkering with the idea" of sending him for a seventh before calling for Juan Carlos Oviedo, who followed with two perfect innings.
"I had probably 10 pitches left," said Bedard, who has allowed one run or less in three straight starts for the first time since 2008. "I'm always a slow starter so the first couple were rough, but after that you just get in the groove of things and throw strikes."
Bedard got nine of his outs on flyballs.
"He just really mixed and matched angles, speeds, everything," said Cleveland manager Terry Francona. "(Raburn) hit the line drive double, but other than that, there was a lot of lazy flyballs. Kind of exactly what he wants you to do."
Zach McAllister (3-3) gave up eight hits and five runs in 4 1/3 innings for the Indians, who had won four straight.
David DeJesus drove in Tampa Bay's first run with a two-out single in the third.
Ben Zobrist had two hits and scored twice for the Rays, who had lost six straight home games.
John Axford is out as the Indians' closer, Francona announced before the game. A group of four relievers that includes Cody Allen, Scott Atchison, Marc Rzepczynski and Bryan Shaw could all get opportunities to fill the role. ... Rays RHP Alex Cobb, who has been on the DL since April 13 with a left oblique strain, is likely to pitch in a simulated game Monday in Port Charlotte, Florida, then make a rehab start five days later. Cobb hopes to pitch for the Rays by the end of the May. ... Indians CF Michael Bourn, as expected, was rested. He played Thursday and Friday after missing three games with a tight left hamstring. ... Rays RHP Chris Archer (2-1) and Indians RHP Josh Tomlin (1-0) are Sunday's scheduled starters.