"Chicago knocked us out last year and they had already clinched, so we wanted to return the favor," Sabathia said. "I was throwing the ball pretty good. I was tying some guys up."
The White Sox fell 1½ games behind Minnesota in the AL wild card race, but remained 3½ behind Detroit in the AL Central. The Twins beat the Tigers 12-1.
After the deflating loss, Chicago headed west for a tough six-game road trip to Anaheim and Oakland that could determine if the defending World Series champions get back in the playoffs.
Martinez's solo shot on a 3-0 pitch from struggling reliever Brandon McCarthy (3-7) put the Indians ahead 3-2 after starter Javier Vazquez pitched strong seven innings for Chicago in a duel with Sabathia.
"You have skids like this, but you'd rather it didn't happen in September when you are in a pennant race," said McCarthy, who's headed to the starting rotation perhaps next season but has been in the bullpen all year.
McCarthy, who gave up three runs without retiring a hitter Saturday night when Chicago nearly blew a 10-1 lead, surrendered two runs and two hits in one-plus inning.
"It stinks. There is no way else to put it," he said of his recent performances. "I'm not happy with the way I'm throwing. ... I'm sick and tired at this point of losing games for this team and today is a prime example - coming in with a big opportunity where I can get something done and again I didn't do it."
The Indians added a pair of insurance runs after Martinez's homer -- his 15th of the season and sixth against the White Sox. Casey Blake hit an RBI single off David Riske and Grady Sizemore drew a bases loaded walk off Sean Tracey. The White Sox used five pitchers in the ninth.
"They don't want to get the leadoff hitter on base walking," said Martinez, explaining his decision to swing at a 3-0 pitch. "I really wanted to make sure to get the head of the bat in front. If you're going to do something on 3-0, make sure to pull it foul."
Sabathia (11-9) gave up a single to Pablo Ozuna and a two-run homer to Tadahito Iguchi -- the first two batters he faced in the first -- but allowed only two hits the rest of the way in running his record to 3-0 against the White Sox this season. He walked two and struck out nine in his sixth complete game of the season.
"He's tough when he's on. One of the best pitchers in the league," Chicago's Paul Konerko said.
"I could have easily lost confidence in my changeup after Iguchi took it deep," Sabathia said. "I just kept throwing it and showing it. It worked out."
Vazquez, coming off one of his best performances of the season, a three-hit, 11-strikeout complete game loss at Fenway Park, gave up an infield hit to Jason Michaels in the first when he beat out a slow roller to short that Juan Uribe couldn't pick up.
He didn't give up another hit until the sixth. He walked Andy Marte with one out and one pitch after White Sox right fielder Jermaine Dye missed catching Sizemore's foul fly against the fence padding, Sizemore hit a triple into the same corner to cut the White Sox's lead to 2-1. Michaels then followed with an RBI single past a drawn-in infield to tie the game.
Vazquez gave up two runs and four hits in seven innings, walking two and striking out 10 while throwing a season-high 127 pitches.
Iguchi's two-run shot, his 15th of the season, extended his hitting streak to 12 games, matching a career high. It came on a 1-2 pitch after he'd failed to get down a bunt.
Sabathia then retired 12 straight before walking Joe Crede to start the bottom of the fifth. But he retired the side by snaring Uribe's liner through the box and easily doubling off Crede.
Chicago didn't get another hit until Iguchi singled over Sabathia's outstretched hand with two outs in the sixth. Dye followed with a broken-bat single to left but Sabathia struck out Jim Thome for a third straight time.
- It was Sabathia's fifth start against the White Sox. He started the season opener April 2 but had to leave in the third inning with a strained oblique muscle that landed him on the disabled list.
- The crowd was announced at 37,723 on a gray and damp day. Rain canceled batting practice.