"I felt really good," Jimenez said. "My first couple innings, I was a little bit off with my fastball and I was falling behind in the count. And they were taking good swings. But as the game went on, I felt a little bit better getting the first pitch for a strike and having better command with my fastball."
Milwaukee struck for two runs against Jimenez in his 5 1/3 innings of work. In the second inning, Logan Schafer scored from third base on a wild pitch for the Brewers' first run. Then, with runners on the corners and two outs, Tribe left fielder Michael Brantley made a diving catch on a fly ball from Norichika Aoki, ending Milwaukee's threat.
Jimenez, who scattered seven hits and ended with five strikeouts and one walk, smiled wide when asked about Brantley's rally-killing catch.
"That was amazing," said the pitcher. "It looked like he's ready for the season."
Jimenez added that pitching in front of the swift trio of Brantley, center fielder Michael Bourn and right fielder Drew Stubbs is going to benefit Cleveland's pitchers.
"As a pitcher, you want to keep the ball down," Jimenez said. "But in our situation, it's not a bad thing if they hit fly balls. Those guys, they're going to get everything. Those three guys, they can fly and they can field the ball. They're going to go get them."
Blake Lalli contributed a run-scoring double off Jimenez in the fourth inning.
Brewers starter Marco Estrada, who has a 0.96 ERA this spring, allowed one run on three hits in 2 1/3 innings. He was expected to log just two innings against the Indians due to pitching on short rest -- a move that lines Estrada up to open the year as Milwaukee's second starter.
"When I was in the bullpen, everything seemed in place, nice and easy, locating really well," said Estrada, who walked three and struck out one. "Then I got out there and was like, 'Oh, man.' I knew I was rushing, but it was hard to stop it. I had to tell myself, 'Slow down, you're going too fast right now.' Once I got out of that first inning, everything fell into place. I thought I made some good pitches."
All three of Estrada's walks came in the first inning, when he issued a free pass to Mark Reynolds with the bases loaded to force in Cleveland's first run.
In the sixth inning, Lou Marson and Ezequiel Carrera each chipped in an RBI single for the Tribe.
Up next: Cleveland has a scheduled team off-day on Tuesday, but rotation hopeful Corey Kluber will pitch in a Minor League game at the team's complex. Right-hander Trevor Bauer -- up against Scott Kazmir, Carlos Carrasco and Kluber for the fifth spot -- will take the mound for the Tribe's next Cactus League contest on Wednesday, when the Indians take on the Angels at 4:05 p.m. ET in Tempe, Ariz.