Sale (3-0) pitched five innings in his first win against Cleveland since May 1, 2012. The left-hander allowed three runs and six hits while throwing 105 pitches.
The White Sox have captured the first two games of their first series of the year against the Indians, who had a 17-2 record against Chicago last season. They play again on Saturday and Sunday.
Indians starter Carlos Carrasco (0-2) was tagged for five runs and six hits in 4 2-3 innings. It was another shaky start for the right-hander, who allowed five runs in 5 2-3 innings of a 7-3 loss to Minnesota in his season debut. Cleveland pitching issued nine walks, including walking in two runs.
Gillaspie hit a sacrifice fly in Chicago's two-run third inning, helping the White Sox build a 3-0 lead. Adam Dunn, who had two hits and walked twice, singled and scored on Alejandro De Aza's base hit in the fourth.
Sale, who went 0-4 with an 8.61 ERA in four starts against Cleveland in 2013, was unable to protect the lead. Asdrubal Cabrera had a two-run double in the fifth, and then scored the tying run on Nick Swisher's single.
The White Sox grabbed the lead for good in the bottom half.
Gillaspie singled in Adam Eaton, and Carrasco was lifted for Marc Rzepczynski after striking out Jose Abreu for the second out of the inning. Rzepczynski walked Dunn to load the bases and then walked in a run as Dayan Viciedo came back from an 0-2 count to give the White Sox a 5-3 lead.
Gillaspie committed an error in the sixth, allowing Michael Brantley to score, but responded with a two-out, two-run double in the bottom half, making it 7-4. Alexei Ramirez added an RBI single for Chicago in the seventh.
Eaton had two hits and scored three times for the White Sox, who finished with 11 hits. Ramirez went 2 for 4.
NOTES: OF Michael Bourn made his second rehab start for Double-A Akron on Friday night. Indians manager Terry Francona said Bourn, who has yet to play this season with a left hamstring strain, would be examined after the game and though Bourn would prefer to return to the big leagues Sunday, Francona said the team may hold off due to the wet conditions expected that day. Bourn was 1 for 5 with a stolen base. ... Indians DH Jason Giambi (broken rib) made his first rehab start on Friday night for Akron. He was 0 for 2 with two strikeouts. ... The White Sox acquired OF Gorkys Hernandez from Kansas City for cash considerations and assigned him to Triple-A Charlotte.