Davis (10-8) struck out eight in his second career complete game.
Jaso put the Rays ahead 3-0 with a three-run homer off John Lackey (12-12) in the second.
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.
In Anaheim, California, Pinch-hitter Maicer Izturis drove home pinch runner Jeremy Moore with a bases-loaded sacrifice fly in the ninth inning, and the Los Angeles Angels rallied to beat the New York Yankees 2-1 Friday night for their fifth win in six games.
Jered Weaver struck out 11 during eight innings of three-hit ball, but the Los Angeles ace left without a victory when his teammates couldn't solve Bartolo Colon, who yielded six hits and an unearned run in seven resilient innings.
After Alberto Callaspo led off the ninth with an infield single off Aaron Laffey (2-2).
Angels closer Jordan Walden (5-3) pitched the ninth, and Howie Kendrick had a run-scoring single as the Angels stayed 21/2 games behind the AL West-leading Texas Rangers.
Rookie Jesus Montero hit his third career homer for the AL-leading Yankees, who have lost three straight-including one loss on each side of the continent in the past two days.
In Toronto, Jeremy Guthrie pitched three-hit ball for seven innings, Vladimir Guerrero and Nick Markakis each drove in a run and Baltimore won its third straight.
The major league leader with 17 losses, Guthrie (7-17) came in having won just once in his past six starts and was seeking to avoid setting a career high for defeats. The right-hander made sure of that in a stellar outing. He walked three and struck out five.
Pedro Strop worked the eighth and Jim Johnson pitched around a leadoff walk to close it out in the ninth for his fourth save.
The hard-luck loser was Blue Jays left-hander Brett Cecil (4-9), who has not won since July 29 against Texas, a span of eight starts. Cecil allowed two runs, one earned, and seven hits in 7 2-3 innings. He walked one and struck out a season-high nine.
In Detroit, Alex Avila hit a three-run homer in the second inning and Ramon Santiago added a two-run shot in the fourth to help the Tigers rally for their seventh straight victory.
Brad Penny (10-10) allowed four runs in the top of the first but settled down after that and Detroit was able to slug its way back from the early deficit. The first-place Tigers have won 17 of 21.
Kevin Slowey (0-5) allowed six runs and seven hits in four innings.
The Twins have lost six of seven and 15 of 19.
In Arlington, Texas, Colby Lewis pitched into the eighth inning for his first victory in nearly a month even while giving up another home run as the AL West-leading Rangers beat Oakland.
Lewis (12-10) trailed 2-0 only four batters into the game after Josh Willingham's two-run homer, the AL-high 33rd allowed by the Rangers' right-hander this season.
Adrian Beltre had an RBI double and Elvis Andrus had two run-scoring hits, including a tiebreaking RBI double in the fifth that made it 3-2.
Brandon McCarthy (8-8) struck out five over six innings, and only two of the four runs against the big right-hander were earned. His fielding error in the first led to one of those runs.
In Chicago, Lonnie Chisenhall set career highs with two homers and four RBIs, and the Indians snapped a four-game losing streak.
Ezequiel Carrera, Kosuke Fukudome, Shelley Duncan and Lou Marson had two hits apiece for the Indians. Carrera and Fukudome each drove in two runs.
Jeanmar Gomez (3-2) allowed two runs and six hits over six innings and improved to 3-0 with a 0.52 ERA in three starts since being recalled from Triple-A Columbus on Aug. 30.
White Sox starter Mark Buehrle (11-8) had his second straight rough outing, allowing seven runs and eight hits over 5 2-3 innings.
In Seattle, Ichiro Suzuki had four hits, including a homer, to help the Mariners beat Kansas City.
Miguel Olivo and Justin Smoak each added three hits for the Mariners. Olivo fell a single short of the cycle.
Blake Beaven (4-5) gave up three runs in 6 1-3 innings, retiring 13 straight batters during one stretch.
Jeff Francis (5-16) allowed five runs in 3 1-3 innings.
