Matt Joyce hit the go-ahead two-run single in a five-run fourth inning, lifting Tampa Bay to a 5-3 win over Boston in the opener of a three-game series
Luke Scott hit an RBI double and Jose Molina added a two-run base hit in the deciding frame for the Rays, who were coming off a weekend sweep of San Diego and won their sixth straight overall.
Matt Moore (7-0) remained perfect on the season and tied for the major-league lead in victories by scattering three hits and as many runs in his six-inning outing. The left-hander also became the first hurler in franchise history to start a season with seven wins before losing a start.
"Matt's been wonderful," Rays manager Joe Maddon said. "We've talked a little bit about the command issue, but he doesn't give up a lot of hits. He might walk a couple of guys, but they're not beating him up with hits."
David Ortiz launched a three-run homer for the Red Sox, who fell to 4-9 in May after an 18-8 start to the season.
John Lackey (1-4) was dented in defeat for nine hits and five runs over just 4 1/3 frames.
All of the Rays' offense came in their fourth turn at the plate, turning a three-run deficit into a two-run edge.
Evan Longoria began the burst with a leadoff single and Loney followed with a base hit to put runners at the corners ahead of Scott's double, which scored Longoria.
Two batters later, Molina dumped a single to center which brought in two more to tie the game at 3-3. Yunel Escobar also singled, then advanced on a flyout before Joyce's single behind first base managed to score two more to make it 5-3 for the hosts.
Lackey was pulled after Loney's one-out double in the fifth, but Andrew Miller closed out the frame fanning Scott while catcher Ryan Lavarnway threw out Loney trying to steal third.
The Sox finally chased Moore after putting two on in the seventh, but Shane Victorino lined out against Josh Lueke to end the threat.
Joel Peralta silenced Boston in the eighth and Fernando Rodney earned his seventh save by striking out the side in the ninth.
Jacoby Ellsbury was plunked to start the game, Dustin Pedroia doubled with two down and Ortiz made it 3-0 with a blast inside the foul pole to deep right field.
"It's frustrating, especially after we score three in that first inning," Pedroia said of the loss.
The Red Sox fell to 10-3 in their first game of a series this year, the second-best such mark in MLB behind the Braves (11-2) ... Pedroia finished 1- for-3, ending his streak of consecutive multi-hit games at five, and failed to match Wil Cordero's run of six in a row from Apr. 28-May 5, 1996 ... Moore matched Washington's Jordan Zimmermann (7-1) for most wins in baseball, while also equaling the feat of Texas' Tommy Hunter (8-0 in 2010) as the only pitchers under the age of 24 to start a season with at least seven wins without losing.