Alfredo Aceves (7-1), who relieved starter Andrew Miller in the sixth, got the victory with one inning of relief.
White Sox star Paul Konerko left the game with a bruised calf after being hit with a pitch by Miller in the bottom of the fourth inning. Konerko initially stayed in the game and took his base, but left after the inning ended. X-rays were negative.
Chicago starter Mark Buehrle pitched six innings, giving up five hits and two runs, both coming on Varitek's seventh homer in the second. The lefty departed with a 3-2 lead.
But the Red Sox threatened in the seventh against reliever Jesse Crain (5-3), as Marco Scutaro singled and Jacoby EIllsbury got an infield single off the mound before backup catcher Tyler Flowers' passed ball allowed both runners to move up.
Pedroia then hit a two-run single to center to put the Red Sox ahead and finish Crain. Chris Sale struck out David Ortiz with runners at second and third to end the inning.
Adrian Gonzalez doubled in a run in the ninth to make it 5-3.
Daniel Bard pitched 1 1/3 innings of scoreless relief and Jonathan Papelbon struck out the side in the ninth for his 24th save in 25 chances.
Alexei Ramirez's RBI single, Chicago's third hit of the inning, gave the White Sox a 3-2 lead in the fourth. Miller then hit Konerko in the left calf with a pitch to load the bases. Konerko stayed down for a couple of seconds and then was able to walk it off and stay in the game.
But he left after the inning ended and was replaced by Brent Lillibridge, who started the game in left. Juan Pierre then moved into the game in left and in Konerko's third spot in the order.
Varitek hit a two-out, two-run homer in the second to give Miller a quick lead.
But Chicago got one back in the second on Brent Morel's two-out RBI double over center fielder Ellsbury's head and another in the third when Carlos Quentin, Adam Dunn and Alex Rios hit two-out consecutive singles.
Miller gave up 10 hits and three runs in his 5 2/3 innings with one walk and a season-high eight strikeouts.
Notes:
The White Sox honored former slugger Frank Thomas by unveiling a statue of the two-time MVP on the outfield concourse. … Bard has not allowed a run in his past 26 1/3 innings. … The White Sox inserted DH Dunn into the lineup at first in the ninth.