The 23-year-old left-hander extended Boston's woes at Tropicana Field on Wednesday night, pitching six strong innings in a 6-4 victory that finished a two-game sweep of the Red Sox and tightened the AL wild-card race.
"We never felt out of it," Price said. "A lot of people counted us out, but nobody in here did."
Facing the Red Sox for the first time since getting the last four outs of last season's AL Championship Series, Price (5-4) allowed two runs and six hits to improve to 5-1 with a 2.72 ERA at home compared to 0-3 with an 8.20 ERA on the road.
Pena hit a two-run homer off Brad Penny (7-6) in the second inning. Crawford, celebrating his 28th birthday, went deep with a man on in the third. Burrell added a solo shot off Penny for a 5-2 lead in the sixth.
Bartlett hit a solo shot off Manny Delcarmen in the seventh.
"They're a good team. I don't think it's this place," Red Sox manager Terry Francona said. "It's who we're playing. They play us very tough."
Jason Bay and Victor Martinez hit solo homers off Price for Boston, which fell 2½ games behind the AL East-leading New York Yankees heading into a four-game series that begins Thursday night at Yankee Stadium.
Price struck out five and walked none.
"David's got a good head on his shoulders. He doesn't get overwhelmed. He just takes care of his business quietly," Boston's Rocco Baldelli said.
"More than anything we came in today thinking, if he gets behind [in the count], we can do some damage against him. We couldn't because he threw strikes and he was in the zone the whole night," Baldelli said.
With the sweep, the third-place Rays (5½ behind the Yankees) continued to close on the Red Sox in the division. Three games separate the teams in the standings, and Tampa Bay leads the season series 8-4, including five of six at Tropicana Field.
Since posting season highs Sunday with 18 runs and 23 hits to complete a weekend sweep at Baltimore, the Red Sox have fizzled offensively. They were limited to homers by Kevin Youkilis and Dustin Pedroia in Tuesday's 4-2 loss to the Rays in 13 innings and struggled again in key situations against Price.
Boston threatened in the third, fourth and fifth against the left-hander but went 0-for-6 with runners in scoring position -- unable to cut into Tampa Bay's lead until Martinez led off the sixth with his 16th homer to trim the deficit to 4-2.
The Red Sox finished 0-for-11 with runners in scoring position. Lowrie grounded out to drive in an unearned run in the seventh, and Youkilis' grounder drove in Boston's final run after Pedroia walked and Martinez doubled in the eighth.
Penny, who's lost four of five decisions over his last eight starts, allowed five runs and six hits in six innings.
The Red Sox agreed to terms on a minor league contract with right-hander Paul Byrd. ... Red Sox designated hitter David Ortiz had the night off. He said before the game that he's still waiting for additional information regarding a positive test for performance-enhancing drugs in 2003. ... One of Tampa Bay manager Joe Maddon's first orders of business was making sure no equipment bags were left on the ground in the team's bullpen in right field. The Rays cost themselves the go-ahead run in the eighth inning of Tuesday night's marathon when Red Sox right-hander Daniel Bard threw wildly past first after fielding a bunt and the ball rolled under a bag and was ruled dead. The umpires "interpreted it right," Maddon said. "It's one of those things if we win, it's OK. If you don't, it's not OK." ... Injured Boston right-hander Daisuke Matsuzaka (right shoulder strain) played long toss and threw at 60 feet on flat ground. He's scheduled for his first bullpen session next week and remains hopeful of pitching again this season.