DETROIT (AP) -- Niko Goodrum and John Hicks were in no mood to wait for a deep count against Trevor Bauer.
"This isn't the time to be patient against a guy who throwing like that," Goodrum said. "He threw me a fastball down and in, and I put a good swing on it."
Bauer allowed home runs to Goodrum and Hicks, who powered Detroit over the Cleveland Indians 4-1 Wednesday for the Tigers' sixth win in seven games.
Bauer (1-1) gave up four runs and 10 hits in 5 2/3 innings. He had allowed one run and one hit in his first two starts.
Miguel Cabrera singled with two outs in the first, and Goodrum sent the next pitch over the right-field wall.
Hicks homered leading off the sixth for a 3-1 lead, Gordon Beckham doubled with one out, and Josh Harrison singled on a bouncer up the middle to chase Bauer.
"That last ball got pounded into the ground about 800 times and just found a hole," Bauer said. "I guess I was due for a correction today after the first two starts."
Matt Boyd (1-1) allowed one run and four hits in six innings with six strikeouts that raised his total to 29 in 17 1/3 innings over three starts.
"Everything is predicated off the fastball," he said. "When I've got a good fastball, it makes all of my other pitches better."
Shane Greene, Detroit's sixth pitcher, got three straight outs for his eighth save in eight appearances, ending Cleveland's five-game winning streak. He became the first big leaguer with eight saves in his team's first 12 games.
"We're going to kill Shane if we keep using him like this," Tigers manager Ron Gardenhire said. "But he wants the ball in every save situation, and we aren't scoring enough runs to get any lopsided wins."
Hanley Ramirez hit an RBI double in the sixth, but Boyd ended the inning by striking out Jake Bauers with runners on second and third.
Joe Jimenez walked the bases loaded with two outs in the eighth. Buck Farmer got pinch-hitter Greg Allen to ground into a forceout.
Gardenhire won his 1,140th game and tied for 50th with Tom Kelly. Gardenhire served as a coach with the Twins under Kelly from 1991-01, then replaced him as Minnesota's manager.
"I can't think of a better man to be tied with," Gardenhire said. "T.K. took me under his wing in Minnesota and taught me so many things, then pushed for me to get the managerial job. I could retire right now, happy I'm next to him in the record book."
Indians: CF Leonys Martin needed lengthy treatment after being on the right hand by a pitch in the sixth inning. He stayed in the game. ... RHP Mike Clevenger (back) was evaluated on Tuesday by Dr. Mark Schickendantz. Clevenger will rest for 6-8 weeks before resuming baseball activities. ... SS Francisco Lindor (ankle, calf) took grounders and did limited running.
Tigers: CF JaCoby Jones (shoulder) had his minor league injury rehabilitation assignment moved from Class A Lakeland to Triple-A Toledo. The Tigers hope Jones, who hit .211 in five games with Lakeland, can make his season debut early next week.
RHP Spencer Turnbull (0-1, 4.09) starts Thursday's series finale for Detroit and RHP Shane Bieber (0-0, 3.38) for Cleveland. Turnbull pitched a scoreless inning of relief against Cleveland in his major league debut last Sept. 14.