The big lefty worked seven strong innings to beat his former team for the first time since signing a $161 million, seven-year contract with New York as a free agent in December.
"Early on, you got the feeling this could be a special night for CC in his return," Yankees manager Joe Girardi said. "He had good stuff and was throwing strikes."
Sabathia, who is 4-0 with a 2.08 ERA in his last five starts, knew the situation.
"Any pitcher who tells you they don't know is lying," Sabathia said. "But I don't know what no-hit stuff feels like. I just know I felt comfortable being back on the mound here. I wasn't nervous."
Sabathia (5-3) allowed three runs, five hits and three walks, striking out eight. And he wasn't surprised by the fans' reaction to his effort. He was neither loudly jeered nor cheered - unlike Thursday night at the Cleveland Cavaliers' playoff game when basketball fans booed him soundly.
"These are baseball fans here and they know how much I cared for their team," Sabathia said. "They know how I tried to play for them. There were a lot of Yankees fans here, too."
Robinson Cano drove in three runs, while Derek Jeter and Johnny Damon had two RBIs apiece as the Yankees opened a 1½-game lead in the AL East over Boston with their 14th win in 17 games.
"It starts with pitching," Yankees third baseman Alex Rodriguez said. "CC had phenomenal stuff. His velocity was up to 98 (mph) with a good changeup. But everybody is contributing. We're 25 men deep."
New York also played its 16th straight errorless game, one short of the major league record set by the Red Sox in June 2006, according to the Elias Sports Bureau.
"It's great to have defense like that behind you," Sabathia said. "Even after I left, A-Rod made a play on a ball that I thought was foul and turned it into an out."
It was a dismal night for Cleveland sports fans.
As LeBron James and the Cavaliers were eliminated in the NBA's Eastern Conference finals at Orlando, the last-place Indians lost their top hitter to an injury.
Cleveland catcher Victor Martinez fouled a ball off his left knee in the first inning and was replaced. The Indians said X-rays were negative and Martinez, hitting .350 with seven homers and 36 RBIs, is day to day with a bruise.
"Victor's a great friend, but that's baseball and you have to focus on your game and forget everything else," Sabathia said.
Sabathia went 106-71 with a 3.83 ERA for Cleveland from 2001-08, including 19-7 with a 3.21 ERA in 2007 when he became the team's first Cy Young Award winner in 35 years. The Indians couldn't sign him to a contract extension a year ago and traded him to Milwaukee in July for a package of prospects.
The 6-foot-7, 290-pounder led the Brewers to their first postseason appearance in 26 years before signing with New York.
The Yankees struck quickly against Fausto Carmona (2-5). Posada opened the second with his sixth homer. One out later, Swisher hit his 10th, over the wall in center.
Indians first baseman Ryan Garko and right fielder Shin-Soo Choo made errors in New York's five-run fourth.
Garko's throwing error loaded the bases and Jeter followed with a two-run single. Damon then singled home a run and Choo bobbled the ball, allowing Jeter to go to third.
With two outs, Cano lined a bases-loaded single for two more runs and a 7-0 lead.
"There were a couple of plays we didn't make that would have helped us," Indians manager Eric Wedge said. "We need to be better than that."
Sabathia allowed only one walk until Choo singled off his pitching hand with one out in the fifth. Garko and Jamey Carroll had RBI singles later in the inning to make it 7-2.
Choo and Grady Sizemore homered for Cleveland. Carmona gave up four earned runs and eight hits over four innings.
Notes: Cano struck out with two on to end the first. It snapped his career-high streak without a strikeout at 54 at-bats. ... Indians DH Travis Hafner, on an injury rehab assignment at Triple-A Columbus, didn't play Saturday because of soreness in his right shoulder.
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