The Tribe trailed 4-3 in the eighth but put runners on second and third with two outs against Donnie Veal (1-2).
Lonnie Chisenhall followed with a single and Yan Gomes (three RBI) capped the four-run rally with a two-run double as the streaking Indians remained 2 1/2 games behind American League Central-leading Detroit.
Bryan Shaw (2-2) earned the decision and Chris Perez secured the victory with his 15th save.
Adam Dunn went 2-for-3 with two RBI for the White Sox, losers of five straight.
2014: The Year in Music [PHOTOS]