Jason Varitek hit a three-run home run and Boston rallied in the eighth and then held on to beat the Rangers, 6-5, to complete their first three-game sweep in Texas in nearly 34 years.
Trailing 6-4 and down to their final out in the bottom of the ninth, Mark Teixeira hit an RBI single into left field, scoring Victor Diaz from second base.
However, Hideki Okajima got Sammy Sosa to fly out to center for his third save of the season.
J.D. Drew went for 2-for-4 with an RBI and two runs scored for the Red Sox, who swept the Rangers for the first time in Texas since August 20-22, 1973.
Kevin Youkilis went 2-for-5 with a run scored to extend his hitting streak to 19 games. Joel Pineiro (1-0) pitched 1 2/3 hitless innings to pick up the win.
Teixeira hit a three-run home run for the slumping Rangers, who have dropped five straight.
Down 4-3 in the eighth, Youkilis singled off Texas reliever Akinori Otsuka (1-1) and stole second as Manny Ramirez struck out. Drew followed with a single to right, scoring Youkilis with the tying run.
Drew went to second on the throw home and then scored on Mike Lowell's single into left field.
Dustin Pedroia gave the Red Sox what proved to be a much needed insurance run in the ninth with a leadoff homer off Texas close Eric Gagne.
Boston struck in the fourth inning on Varitek's fourth home run of the season. Drew and Lowell led off with back-to-back singles and Varitek crushed a 1-1 pitch over the right field wall to make it 3-0 Boston.
Red Sox starter Julian Tavarez, meanwhile, gave up just one hit through five innings before running into trouble in the sixth.
Tavarez walked Kenny Lofton to start the inning and Michael Young singled to center. Teixeira followed with his ninth homer of the season to tie the game at 3-3. Frank Catalanotto, Marlon Byrd and Ian Kinsler then hit three consecutive singles, with Catalanotto scoring on Kinsler's base-hit to give Texas the lead.
Tavarez finished with four runs allowed on six hits through 5 2/3 innings. He also struck out six and walked one batter.
Rangers starter Kameron Loe pitched six innings, yielding three runs on seven hits.
Texas had a chance to build on its lead in the seventh, but Red Sox center fielder Coco Crisp made a sensational grab on Catalanotto's line drive to center with two outs and runners on first and second.
Lofton finished 2-for-3 with a double for the Rangers...Sosa remains two home runs shy of 600 for his career...Attendance was 40,323.