Jason Giambi's pinch-hit leadoff homer in the bottom of the ninth sent Cleveland past Chicago, 3-2, in the opener of a four- game set.
Batting in place of Mark Reynolds, Giambi's winner touched down beyond the wall in center. It gave the 42-year-old a major league record as the oldest player to hit a game-ending home run, replacing Hall of Famer Hank Aaron.
"Walk is just as good as a hit there to try to get that leadoff guy on," Giambi said. "I wasn't trying to do too much. I just wanted to see it and kind of hit it. I got a pitch up in the strike zone and ended up catching up to it."
Ramon Troncoso (1-3), who turned in a scoreless eighth inning, served up the deciding blast in defeat.
Chris Perez (3-1) stranded a runner on second in the top of the ninth for the win.
Carlos Santana and Asdrubal Cabrera knocked in a run each for the Indians, who stretched their win streak to five games.
Adam Dunn and Paul Konerko drove in the runs for the White Sox, who dropped their fourth straight game and seventh in eight.
The Tribe hit the scoreboard in the second. Cabrera reached on Connor Gillaspie's throwing error, moved to third on a Ryan Raburn double and scored on a Santana fly to left.
Chicago sprang to life in the sixth, going on top with a pair of runs with two out thanks to Dunn's RBI double and Konerko's RBI single. However, the hosts evened the score in the home half.
Michael Bourn and Nick Swisher walked, then Jason Kipnis bunted for a hit to load the bases. Cabrera's hot shot deflected off Alexei Ramirez at short, but Gordon Beckham threw in time to first, allowing Bourn to come in for a 2-2 game.
Cleveland has won eight of 10 games against the ChiSox this season ... Tribe starter Zach McAllister gave up five hits and two runs over seven innings, while Chicago counterpart John Danks worked six-plus frames and gave up two hits and one earned run, walking four ... The White Sox fell to 23 games under .500 for the first time since Sept. 11, 2007 ... The Indians have scored first in 16 consecutive games, setting a franchise record. It is the longest for any team since Milwaukee scored first in 21 straight in 1990.