"It's actually the first time I've really started throwing a cutter," Davis said. "I've always thrown a slider and we just flattened it out a little bit to stay in the strike zone more. It ended up being pretty effective."
Davis (10-8) struck out eight in his second career complete game. The right-hander, who had his other complete game on Sept. 17, 2009, had gone 0-2 with an 11.12 ERA in three previous starts against Boston. Tampa Bay pitchers have 15 complete games this season.
"He had a pretty good cutter going," Red Sox manager Terry Francona said. "Threw it outside, inside and just ate us up."
Jaso put the Rays ahead 3-0 with a three-run homer off John Lackey (12-12) in the second. He entered 8-for-37 (.216) in 14 games since returning from a strained right oblique last month. Boston has lost five of six.
After two more games in Florida this weekend, the Red Sox will host Tampa Bay in a four-games series that starts Thursday at Fenway Park.
"We do believe," Rays manager Joe Maddon said. "It's all about one at a time. But obviously we have to make a big dent with these seven games."
The Red Sox were without infielder Kevin Youkilis, who returned to Boston to have his sore hip examined by team doctors and undergo an MRI exam.
Francona said Youkilis has bursitis and received a cortisone shot. It has not been determined if Youkilis will rejoin the team Saturday or wait in Boston for the start of a homestand that begins Tuesday.
Rays designated hitter Johnny Damon was back in the lineup after missing the previous three games because of a sore right leg. He had an infield single during the third that moved him past Doc Cramer into 62nd place on the all-time hits list with 2,706.
Damon and Matt Joyce had RBI singles in the third to made it 5-0. Jaso later in the inning hit a two-out shot with the bases loaded off Lackey's left leg, but the pitcher recovered to pick up the ball and throw the Rays' catcher out at first.
Lackey left with a bruised calf and was replaced by Scott Atchison to start the fourth. Lackey, who has lost three consecutive starts, gave up five runs, five hits and three walks in a 69-pitch outing.
"It hit him good," Francona said. "It's sore."
The Red Sox have not ruled out Lackey making his next scheduled start.
"They don't quit," Maddon said of Boston. "They have the heart of a champion."
Tampa Bay has won 19 in a row when scoring five runs or more. ...The Rays are just the fifth AL team since 2000 to reach 15 complete games in the same season. . ... Francona said RHPs Clay Buchholz (lower back) and Josh Beckett (sprained right ankle) are making progress. A schedule for when Buchholz could throw off a bullpen mound may be determined this weekend. ... Boston recalled Atchison from Triple-A Pawtucket before the game. ... Red Sox RHP Kyle Weiland (0-1) and Tampa Bay RHP Jeremy Hellickson (12-10) are Saturday's scheduled starters.