Jacoby Ellsbury recorded Boston's first hit with a go-ahead two-run homer in the sixth inning, sparking the Red Sox over the free-falling Tampa Bay Rays, 5-2, in the opener of a four-game set.
Ellsbury added an RBI single in Boston's three-run seventh to back a quality start by Aaron Cook (4-10), who won for the first time since Aug. 6 by allowing just one run on five hits over six innings.
Boston has been mathematically eliminated from the playoffs, and the Rays are playing themselves out of contention with six losses in their last seven games.
Coupled with last week's 1-5 road trip against the Yankees and Orioles, Tampa Bay sits five games behind Baltimore for the final AL wild-card spot.
Rays starter Alex Cobb (9-9), trying for a sixth straight winning decision, was charged with four runs -- three earned -- on two hits and three walks over six-plus innings.
Cobb did not allow a hit through five innings and was working with a 1-0 lead after Luke Scott scored on Ryan Roberts' suicide squeeze in the fifth.
But Cobb plunked Jose Iglesias in the sixth and grooved a 3-1 pitch to Ellsbury with two away. Ellsbury turned on the fastball and sent it deep into the right-field bleachers for his fourth home run of the season.
"(Cobb) was pitching great, hitting his spots and throwing his changeup," Ellsbury said. "I was just trying to relax, trying to go up there focused."
Cobb and his backstop, Jose Molina, got into a short shouting match in the dugout after the inning, and Rays manager Joe Madden pulled his starter after he put the first two hitters on in the seventh.
Burke Badenhop came in from the bullpen and induced a tailor-made double-play ball off the bat of Ryan Lavarnway. But Ben Zobrist, making his 32nd start at shortstop this year, booted the soft grounder.
With the bases now loaded, J.P. Howell came in and gave up a pair of RBI hits, the first a two-run single to pinch-hitter Mauro Gomez. Ellsbury came up later with the bases loaded and singled to left to bring in another run for a 5-1 cushion.
Rich Hill and Junichi Tazawa each threw a perfect inning of relief behind Cook, and Mark Melancon gave up a run in the home ninth.
B.J. Upton led off the frame with a base hit, moved to second on defensive indifference and advanced further on a wild pitch. Zobrist's groundout to short allowed Upton to score, and Melancon struck out Matt Joyce and pinch- hitter Ben Francisco to end things.
"We just didn't score any runs," Upton said.
Cook, who had lost his previous five decisions, has tossed less than 100 pitches in 41 straight starts since July 1, 2010 ... The Rays are 8-14 since they were a season-high 15 games over .500 (70-55) on Aug. 23 ... The Rays went 0-for-2 with runners in scoring position and have hit .153 (9-for-59) with RISP in their last 10 games ... Attendance: 11,722.