No problem, said southpaw specialist Rich Hill, who came on and got Luke Scott on a flyout to left.
Though the bullpen buckled ever so slightly in the eighth, giving up a run on a bloop RBI single by B.J. Upton, closer Alfredo Aceves made sure it didn't get any further, inducing Scott into an inning-ending groundout.
Aceves (1 1/3 innings) also worked the ninth to record his eighth save.
In all, Valentine used five relievers, matching up frequently and bringing his team safely to the finish line.
"Yeah, I was going with the matchups. I wanted to win that game," said Valentine. "I was going after this game tonight. I thought the guys really wanted this game. I was going to do everything we could to win it, not that I don't manager that way every day, but sometimes I'll take some future considerations. There weren't any future considerations today."
In the past five games that the Red Sox have used their bullpen, the relievers have allowed just one run over 14 1/3 innings.
"Super," Valentine said. "They're getting ready, they're coming in, they're throwing strikes. They know their job. They're passing the baton. I'm proud of them. They should be proud of themselves. They're being highly professional."
With the win, the Red Sox salvaged a split of this two-game series against the Rays, who are just one game behind the American League East-leading Orioles.
Boston is 6 ½ back in the division, still trying to recover from a disappointing start. With six wins in their last seven games, the Red Sox now travel to Philadelphia for a three-game weekend series and a reunion with former closer Jonathan Papelbon.
"It definitely wouldn't be good coming in here and dropping the first two on a tough road trip, going to Philly and then Baltimore is in first place," said outfielder Cody Ross. "We know how good these guys are. We have to play every single pitch like it's our last. Today was a perfect example of a really good team win."
Doubront turned in another solid performance, scattering six hits and two runs over 5 2/3 innings. Doubront walked four and struck out seven to improve to 4-1.
"Pretty good," Doubront said. "I feel like everything was good. When that happens, you see the results."
One night after saying he cost his team a game when he lost a ball in the Tropicana Field roof that resulted in a go-ahead sacrifice fly, Ross came up big for Boston.
The outfielder belted a solo homer in the third and an insurance two-run single in the eighth. He had four RBIs on the night.
"I obviously felt really bad about last night," said Ross. "It was just a tough play. To come out today and pick up the team [and] get a victory to split the short series is real big for us."
Ross walked with the bases loaded in the first against Rays phenom Matt Moore to give Boston a 1-0 lead.
"Terrific," said Valentine. "Got him off of the 0-2 fastball after the two changeups and then took the changeup on 3-2 like he was totally controlling the at-bat. He was terrific I thought."
In the second, Marlon Byrd went deep, roping a solo shot to left. It was Byrd's first homer after a drought of 126 at-bats, dating back to Sept. 21, 2011.
If you blinked, you might have missed Byrd running around the bases. It certainly wasn't a home run trot.
"It's a tribute to Scott Rolen," Byrd said of his former Phillies teammate. "He gets around fast."
Ross ripped his solo shot just over the wall in center, his seventh home run on the year. That made it 3-0.
The Rays chipped back into it against Doubront. They had some good fortune in the third, when Upton came up with two outs and nobody on and reached on catcher's interference. Scott was hit by a pitch. That set up Jeff Keppinger, and he delivered, smashing an RBI single to center.
In the fourth, Tampa Bay cut Boston's lead to 3-2 as Rich Thompson delivered his first Major league hit, a two-out RBI single.
Back in April, this would have been the type of game Boston would have had a tough time winning, but things are changing for Valentine and Co.
"They pitched well, they pitched really well," said Rays manager Joe Maddon. "They pitched well last night, too, and lost. Their bullpen, from what I've read, has been doing a lot better. To me, the key is they've got some lefties who can get a lefty out with the big guy, [Andrew] Miller, [Franklin] Morales, great arm, and then Hill, has a big sweeping breaking ball, and Aceves. They have a nice balance between the right- and left-handed pitchers."