Javier Vazquez (5-3) overpowered a struggling Indians lineup with seven strikeouts in seven innings. He allowed two runs on four hits and ended his outing by striking out Jhonny Peralta.
Jim Thome followed Dye's eighth home run of the season in the seventh with his second homer in as many days and ninth on the season.
With a 2-0 lead in the sixth inning, Indians starter Paul Byrd (2-4) allowed a leadoff single to Orlando Cabrera and walked A.J. Pierzynski.
Carlos Quentin followed with a sharp grounder to third baseman Casey Blake. Blake started what could have been a 5-4-3 double play, but Pierzynski went in hard at second, putting pressure on second baseman Asdrubal Cabrera.
Cabrera got off a clean accurate throw, but first base umpire Paul Schrieber called Quentin safe. After Indians manager Eric Wedge argued the call, Dye hit a 2-1 pitch into the left field seats, putting the White Sox ahead.
Thome and Paul Konerko chased Byrd (2-4) in the sixth with back-to-back singles. Joe Crede greeted Indians reliever Jorge Julio with an RBI double and Alexei Ramirez added a sacrifice fly to give the White Sox a 5-2 lead.
Byrd allowed five runs on five hits in 5 1-3 innings. He struck out two and walked one.
He was cruising until the fifth inning. He only threw 55 pitches until the sixth and didn't allow his first hit until Nick Swisher singled in the fifth.
Travis Hafner hit an RBI double in the sixth inning off Vazquez.
Notes: Aubrey, who made his major league debut on Sunday, has homered in his first two major league starts. ... Indians LF David Dellucci made a leaping catch near the fence in left in the fifth inning, robbing Crede of extra bases. ... Dye had his 18th career two home run game. ... Thome has homered four times in five games against his former team.
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