The left-hander, who had seven strikeouts, retired 16 in a row after Norris Hopper hit a two-out, RBI single in the second.
"Just to see the sixth, seventh inning is definitely big," Sabathia said. "Go out there and get used to it."
Cincinnati starter Aaron Harang gave up four runs - two earned - and four hits over six innings. The right-hander is set to become the first Reds pitcher to make four straight opening-day starts since Jose Rijo (1992-95).
"That's the best I've thrown all spring, with the life I had on the ball," Harang said. "We had a couple of errors that prolonged the one inning. Other than that, I felt good."
Sabathia will have his final spring training outing Wednesday against Philadelphia. He will pitch in the Yankees' regular-season opener April 6 at Baltimore, and will also throw the first regular-season pitch at the new Yankee Stadium 10 days later against Cleveland.
"He's fun to catch," Yankees catcher Jorge Posada said.
Harang, also scheduled to make one more preseason start, struck out five and walked two.
"I'm at the point now where my arm strength's built up, I got through 101 pitches," Harang said. "I felt like if I had to, I could have gone back out there for another inning."
Reds third baseman Edwin Encarnacion and shortstop Alex Gonzalez didn't make the trip.
Encarnacion has been sidelined for a week by a sore throwing shoulder, hurt while diving for a ball. Cincinnati manager Dusty Baker expects to use him on Saturday as a designated hitter against Tampa Bay.
Gonzalez, who worked out at the Reds' complex in Sarasota, strained his right hamstring on Monday. Baker expects him to miss at least one more game.
"We don't want to put him out there and have to shelve him again," Baker said. "It's hard to tell when those hamstrings heal."
Baker had been using Gonzalez cautiously this spring because the shortstop is returning from a knee injury that sidelined him all last season.
"I've still got to get him back-to-back days," Baker said. "I was still in that process when this happened. He was going to go nine (innings) one day, then a day off, then go back-to-back days.
This set him back a little bit."
Yankees closer Mariano Rivera needed just five pitches to work a perfect ninth that included one strikeout. Coming back from right shoulder surgery last October, Rivera has given up one hit and struck out seven over five shutout innings overall.
"Feeling good, that's the bottom line," Rivera said. "It's been real good."
Rivera expects to pitch in one of the exhibition games against the Chicago Cubs next Friday and Saturday at the new Yankee Stadium.
Mark Teixeira had a run-scoring single for the Yankees.
Notes: Actor Richard Gere threw out the ceremonial first pitch. ... Yankees manager Joe Girardi said "it's a pretty good possibility" that CFs Brett Gardner and Melky Cabrera will both be on the opening-day roster. Gardner is thought to be the front-runner for the starting spot. ... Reds LHP Daniel Ray Herrera worked a perfect seventh. He has retired 22 of the 23 batters he's faced this spring. ... New York RHP Chien-Ming Wang will pitch in a minor league game on Saturday. The three contenders for long relief spot - Brett Tomko, Alfredo Aceves and Dan Giese - will pitch in Saturday's road game with Atlanta. ... The Yankees will dedicate a 9-11 memorial, that includes a steel beam from the World Trade Center, outside George M. Steinbrenner Field before Sunday's game.
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