Bauer gave up four hits, including a home run to Tyler Flowers, in 6 1-3 innings. He fanned Melky Cabrera and Adam LaRoche three times apiece but walked his first batter of the spring, Adam Eaton.
This outing, he said, was about "trying to get into a season mindset, get guys out more so than working on stuff.
"The things that I worked on early in spring, I was able to execute today and put into use," he added.
Bauer, the Arizona Diamondbacks' first-round pick in 2011 out of UCLA, is coming off a 5-8 season with a 4.18 ERA in 26 starts for the Indians.
One area he wants to improve in was his effectiveness in the first inning. Last year he had a 5.54 ERA in the opening inning, often putting himself in an early hole.
"It's been a point of emphasis this offseason, doing some research on what was going on in the first inning," Bauer said. "It's spring training, you never know until you get into the season. So far, I'm encouraged by it. We'll see how it carries over."
Bradley Zimmer hit a two-run homer to the right field bullpen off Hector Noesi in the fourth. The homer was the first of the spring for Zimmer, an outfielder who was Cleveland's first-round pick — 21st overall — in last June's draft.
Veteran catcher Brett Hayes followed Zimmer's long ball with his third of the spring, a long drive over the bullpen in left.
Noesi went 5 1-3 innings and gave up five hits, walking two and striking out five.
Jerry Sands also homered for the Indians, off Zach Duke.
Indians: Bauer lowered his spring ERA to 3.90 in 22 2-3 innings. He has one start remaining before the Indians open the season in Houston.
"I thought he was really good," Cleveland manager Terry Francona said. "He's starting to get deep into the game and he's starting to mix all his pitches in now. The timing's about right."
The improved control also got Francona's attention.
"That's been great. Love that. Love when guys work quick and throw strikes," Francona said.
White Sox: Noesi, likely to be Chicago's No. 5 starter, went 5 1-3 innings and gave up five hits, walking two and striking out five.
The White Sox sent RHP Chris Beck to minor league camp and released pitchers J.D. Martin and Joe Savery.
The Indians sent outfielder Tyler Holt to Triple-A Columbus.
White Sox: GM Rick Hahn said before Monday's game that reliever Jake Petricka will "in all probability" begin the season on the disabled list. The White Sox think the right-hander, who has had soreness in the forearm/elbow area, could be ready as soon as he is eligible to come off the DL, which would be April 11.
"We don't foresee this being a long-term problem," Hahn said.
White Sox: Carlos Rodon makes his final start of the spring Tuesday against the Dodgers at Camelback Ranch. Last year's third overall pick is coming off a nine-strikeout, four-inning outing against Kansas City.
Indians: Veteran lefty Bruce Chen faces Felix Hernandez and the Mariners on Tuesday in Goodyear.