Chicago was able to seal the victory and win two of three from Oakland with three more runs in the ninth, including a two-run double from Paul Konerko off closer Huston Street.
Dye came into the game batting .100 (2-for-20) and on a 0-for-9 streak, and picked the right game to hit his first homer of the season.
"At that point, when you're struggling, you're just trying to get the good part of the bat on the ball and just stay up the middle," Dye said. "I got a pitch that I was able to drive and didn't foul it off and drove it out of the park."
"Finally," added Buehrle with a smile. "I've been getting on Jermaine. He told me before the game that he always picked me up. When he [played for Oakland] he always seemed to hurt me, when he's on my team he always picked me up. We definitely need those guys in the middle of the lineup to drive in those runs."
Dye's homer seemed to wake up the bats for the White Sox, who had just managed just two runs in 16 innings before his slam to dead-center field.
The A's sent their best pitcher out of the bullpen in Street for the ninth, but the Sox were able to draw two walks to get the middle of the lineup to the plate.
A.J. Pierzynski showed the keenest eye by laying off two outside pitches that could have gone either way for Street.
"They're were close," Street said. "Sometimes you get those calls and sometimes you don't. Those were two pretty good takes on A.J.'s part."
After a four-pitch walk to Scott Podsednik that loaded the bases, Darin Erstad was able to give the White Sox their first lead of the game with a fly ball to left that scored Juan Uribe.
Closer Bobby Jenks showed his short-term memory by closing the door in the ninth for his second save of the year after getting his first loss and blown save on Tuesday night.
"That's one thing that is nice about this game," said Jenks, who struck out Mike Piazza and Mark Ellis in the ninth. "You can make up for the day before. We made some pretty good decisions out there."
Buehrle wasn't able to earn his first win at the Coliseum but he definitely showed that he was at full strength after getting nailed in his forearm on a comebacker on Thursday.
"The past couple days I felt [some] throbbing every time I threw," Buehrle said. "But it didn't bother me one bit."
It was hard to tell that during the first inning when the southpaw gave up three doubles and three runs to start the game, but Buehrle settled down quickly and gave up just one hit the rest of the way.
"Today was one of those days that I threw every pitch where I wanted to," said Buehrle, who went 1 1/3 innings against the Indians. "It was sort of amazing out there. To be able and get out there and go more than one inning feels pretty nice."
"We had a great start," added A's manager Bob Geren. "But Buehrle settled in and pitched really well. His last 70 or 80 pitches were pretty pinpoint."
Buehrle retired nine straight at one point and 16 out of 17 after walking Marco Scutaro in the second inning. With Jenks' ninth and David Ardsma earning the win with a quick eighth inning, Chicago retired the final 13 batters.
The series win against Oakland improved the White Sox record to 16-38 against the A's over the last six years and 6-24 at McAfee Coliseum.
"That was an easy game to give up on and throw away," Konerko said. "We were down 3-1 ... It was an easy one that we could have mailed in. [But] J.D. he got the big hit to tie it up.
"This is probably the earliest we've played [the A's] over all those years. Every team is still finding out the team they are going to be. It's good to catch them before they're the good team they're going to be. We'll take the series win."