Cowgill played in 50 games last season for the Angels after coming from the New York Mets in a midseason trade.
Grant Green, competing for a job as the Angels' utility infielder, played third base and had two hits.
"Grant is looking real strong on the left side of the infield," Angels manager Mike Scioscia said. "He generates some bat speed. He leverages the ball well. Grant hit the ball hard today. I don't know if he'll ever hit 20 home runs but he can drive the ball at times."
The outing was a setback for Bauer, who is trying for the Indians' fifth spot in the rotation. He had allowed just two runs in five innings coming into the game.
"Trevor didn't command. He's throwing the ball real well." Indians' manager Terry Francona said. "He's not locating the ball and working from behind. It's not always going to be easy. Nobody is going to remotely give up. We still think there is a good major league pitcher in there. We are going to have to keep fighting and we'll fight with him. We'll figure it out."
Danny Salazar, who impressed the Indians late in the season, made his first start of the spring. He gave up one run on two hits and two runs in 1 2/3 innings.
Michael Bourn made a running catch of Green's long drive to straightaway center field with the bases loaded to save Salazar from being charged with more runs.
Indians: Salazar worked three innings in a minor league game on Friday. Salazar, who started last season with Akron in Double-A, was supposed to pitch three innings Monday but left with the bases loaded and two outs in the second.
"It was a little bit different seeing batters from a different team," said Salazar, who has been brought along slowly this spring. "I was a little wild but I felt strong. I've been on a program to build for the season."
The 24-year old, who can throw his fastball at 100 mph, looked fine to Francona.
"I thought the ball came out of his hand really well. He was free and easy. There is a lot to build on," Francona said.
Angels: Jared Weaver is making his third start of the spring. He pitched four innings in his last start last Wednesday against the Giants. Weaver threw 72 pitches through four inning but went out for one out in the fifth to "see what it felt like." The 4 1/3 innings was his longest outing to date.
"There were strides made," Weaver said. "I got some balls up but that will be sharper later. I was working on things, throwing more fastballs inside than I usually would. The last start of the spring, I'll pitch like I would during the season."
Angels: Outfielder Josh Hamilton strained his left calf during a running drill a week ago. He took batting practice for the first time on Sunday. ... RHP Dane De La Rosa left the game on Thursday with a strained right forearm.
Indians: Outfielder Ryan Raburn has a bruised left knee after running into the right field wall on Friday. Francona plans to bat Raburn as a designated hitter in a `B' game on Tuesday. ... Right-hander Matt Capps is a few days away from starting a throwing program. He was slowed by a sore rotator cuff. ... Right-hander Frank Herrmann has thrown bullpens on March 2 and 7 without pain. He is 11 months into recovery from right elbow surgery.
Matt Long had four hits, including a double and triple for the Angels. The Angels are short of outfielders with Hamilton out. The 26-year old non-roster invitee has been impressive after a good 2013, in which he was promoted from Arkansas to Salt Lake City after 32 games.
"He is going to play in the major leagues at some point," Scioscia said. "Matt's a gamer. He's been under the radar but he had a good year and made his way into the big league camp."
Mike Aviles was 0 for 3 for the Indians, playing in right field to drop his spring average to .375. Aviles may soon see time in center field.
"Mike understands that he can get more at-bats if he moves around," Francona said. "Sometimes a guy gets to a certain place then levels off. Mike is awesome. He keeps working and has a great attitude. It might not be what he envisions but he can have a nice career."
The Indians used an extreme shift on at least two batters, Raul Ibanez and Carlos Pena. Third baseman Carlos Santana was up the middle just to the left side of second base. Shortstop Erik Gonzalez was up the middle just to the right side of second base. Second baseman Jason Kipnis was pulled toward first and stood in shallow right field, while first baseman Nick Swisher guarded the first base line. The outfield played straight away.
The Angels also shifted the infield for Swisher's at-bats.