Two batters into the game, Sabathia (11-9, 3.24 ERA) was down, 2-0, as he yielded a leadoff single to Pablo Ozuna and homer to Tadahito Iguchi.
The left-hander then yielded only two sixth-inning singles and two walks the rest of the way, striking out nine.
Sabathia is 3-0 with a 2.86 ERA against the White Sox this year, but only 1-0 in three starts in Chicago.
"Chicago knocked us out last year and they had already clinched, so we wanted to return the favor," Sabathia told The Associated Press. "I was throwing the ball pretty good. I was tying some guys up."
Cleveland went only 5-14 against the White Sox a year ago. The White Sox fell 1½ games behind Minnesota in the AL wild card race and remained 3½ behind first-place Detroit in the AL Central.
Martinez (.310) sparked a three-run rally by leading off the ninth inning with his 15th homer on a 3-0 pitch from Brandon McCarthy to break a 2-2 tie.
The switch-hitter is batting .297 (19-for-64) with six homers, 16 RBI and 10 runs against the White Sox this season. He's done most of his damage at Chicago's Cellular Field, going 15-for-41 (.366) with all the homers, 13 RBI and eight runs.
The Indians scored twice more in the inning off a parade of Chicago relievers.
Ryan Garko (.315) singled off McCarthy, who was replaced by Neal Cotts. Shin-Soo Choo (.280) bunted Garko to second and David Riske came on for Chicago.
Casey Blake (.293) greeted the former Indians right-hander with an RBI single to make it 4-2 before Riske struck out Hector Luna (.280).
Boone Logan then came on and issued three straight walks to Joe Inglett (.270), Andy Marte (.225) and Grady Sizemore (.295) to force in another run.
The Indians scored twice off starter Javier Vazquez in the sixth to tie the score, 2-2.
Marte drew a one-out walk and scored on a triple by Sizemore. Jason Michaels (.273) followed with an RBI single.
The four-hitter was Sabathia's second of the season to go with a pair of three-hitters. He lowered his ERA in day games to 2.00, best in the majors and improved to 6-0 at Cellular Field and 11-3 overall in his career against Chicago.
Over his last 36 starts since Aug. 1, 2005, Sabathia is 20-10 with a 2.93 ERA.