Sabathia (3-0) allowed five hits, struck out 10, walked three and improved to 14-3 - 2-0 this season - in 22 starts against Chicago.
"It was cold," Sabathia said. "Guys kind of think twice about swinging when it's cold and you are coming in there."
The Indians' only hit was Grady Sizemore's double in the first off Jose Contreras (1-2). Cleveland took advantage of three errors and some walks to take two of three in the series.
Joe Borowski worked the ninth for his fifth save, striking out pinch-hitter A.J. Pierzynski with a runner on first to end it.
Contreras did a remarkable job of keeping the game close, considering the White Sox made three errors behind him and he walked five in the first four innings.
The right-hander allowed only Sizemore's hit and was able to get big outs when he needed them. However, Contreras ran into trouble again in the fourth with a leadoff walk and an error by third baseman Joe Crede.
Contreras walked No. 9 hitter Kelly Shoppach to load the bases and then put on Sizemore, giving the Indians a 2-0 lead.
The last time the Indians won while getting one hit or less was on April 12, 1992, a 2-1 victory over Boston when they were no-hit by Red Sox pitcher Matt Young.
"That's not something you see every day," said Sizemore, who like Sabathia wore No. 42 in honor of the 60th anniversary of Jackie Robinson breaking baseball's color barrier. "I don't recall ever winning a game with just one hit."
TORONTO - John McDonald drove in the go-ahead run with a seventh-inning single and Josh Towers recovered from a shaky outing with seven-plus strong innings for Toronto.
McDonald broke a 1-1 tie with a two-out single that brought in Royce Clayton, who ran through third base coach Brian Butterfield's stop sign and scored without a play at the plate.
Shaun Marcum worked a perfect ninth for his first career save.
Towers (1-1) scattered three hits over 7 2-3 innings to win a start for the first time since last May 14 at Tampa Bay. He retired 12 straight batters between the second and seventh innings.
Nate Robertson (2-1) lost for the first time in three starts, allowing two runs and seven hits over seven innings.
The Blue Jays placed closer B.J. Ryan on the 15-day disabled list with a sprained elbow, a day after he blew his second save in his past four chances.
MINNEAPOLIS - Dioner Navarro hit a tiebreaking double off Joe Nathan in the ninth inning and Tampa Bay earned a split of the four-game series.
Navarro's second hit of the game snapped a 4-all tie and sent Nathan (1-1) to his first loss since September 6, 2005.
Akinori Iwamura greeted Nathan with a double and scored on Navarro's double. Carlos Pena's RBI single made it 6-4.
Brian Stokes (1-2) worked a scoreless eighth and Al Reyes struck out two in a perfect ninth for his fourth save.
Delmon Young extended his AL-leading hitting streak to 12 games with a two-run homer in the sixth inning .
SEATTLE - Jose Vidro homered in his first two at-bats, and Ichiro Suzuki had four hits for Seattle, which reached a season high in runs.
Suzuki led off with his 21st career home run and one out later Vidro connected for a solo shot, quickly erasing a 2-0 deficit. Vidro added a three-run homer in the second.
It was the 26th career four-hit game for Suzuki, who snapped an 0-for-13 slump Saturday.
The top three hitters in Seattle's order - Suzuki, Adrian Beltre and Vidro - were 9-for-14 with 10 RBIs and nine runs scored.
Horacio Ramirez (1-0) allowed a run in six innings for the win. Texas starter Brandon McCarthy (1-2) lasted two innings, giving up six runs and six hits.
OAKLAND, Calif. - Marco Scutaro hit a three-run homer with two outs in the ninth inning off Mariano Rivera to give Oakland its first series victory of the season.
Scutaro's shot spoiled a strong start by Andy Pettitte, who allowed five hits and two runs - one earned - in seven innings.
Rivera (1-1) blew his first save chance of the season, despite retiring the first two batters in the ninth. Todd Walker singled for Oakland's first hit since the third inning and Jason Kendall then walked, bringing up Scutaro.
Oakland right-hander Rich Harden struck out seven through six innings, then left with tightness in his pitching shoulder. Jay Marshall (1-0) pitched 1 1-3 scoreless innings for his first major league win.