CLEVELAND -- The Detroit Tigers have been a major headache for the Cleveland Indians in recent years. This year might be different.

Trevor Bauer and four relievers combined on a five-hitter and Michael Brantley had four hits as the Indians completed a three-game sweep of the Tigers with a 9-4 victory Thursday night at Progressive Field.

Cleveland banged out 16 hits, scoring four runs in the first inning, one in the fourth and four in the eighth. The Indians' pitchers took it from there. In the last two games of the series Indians pitchers held the Tigers, who rank second in the American League in hitting, to a .159 batting average.

The Indians swept their second three-game series this season against Detroit. The Indians were 7-11 against the Tigers last season and 19-37 over the last three years but they are 6-0 against the Tigers so far this season.

"We need to play better in our own division and we've done a good job of it so far," said Cleveland manager Terry Francona, whose team is 8-3 vs. Central Division opponents.

"They've out-played us. They out-pitched us, out-hit us and out-defended us, period. They've been the better team in all six games," Detroit manager Brad Ausmus. "I'm not happy with the way we've played Cleveland home or away."

Bauer (2-0) was making his second start since coming out of the bullpen to take the place in the rotation of Carlos Carrasco, who is on the disabled list with a strained hamstring.

Bauer pitched 5 2/3 innings, giving up three runs on three hits with four strikeouts and two walks. He threw 106 pitches.

"When he pitched ahead he was really good," Francona said. "They weren't getting hits off him, but he had a lot of deep counts, so his pitch count was up."

Relievers Jeff Manship, Zach McAllister, Bryan Shaw and Joba Chamberlain followed Bauer to the mound.

"This was a huge win for us, to win the series," Bauer said. "The last couple of years it feels like every time we played them we'd get bludgeoned. We didn't just get beat, we got beat bad."

Rookie Michael Fulmer (1-1) gave up five runs and 10 hits in five innings to take the loss in his second major league start for the Tigers.

"He had trouble commanding his fastball in the first inning, but then he settled down and gave us some length," Ausmus said.

Leading 5-3, the Indians added four insurance runs in the eighth inning on a pair of two-run doubles, by Rajai Davis and Brantley to make it 9-3.

"It's important to play well against everyone, but they are in our division, so it's even more important," Brantley said.

Detroit scored its last run on an RBI single by Jarrod Saltalamacchia in the ninth inning.

Fulmer struck out the side in the first inning, but not before he gave up five consecutive hits and four runs.

With one out Jason Kipnis singled to right and went to second on a single to center by Francisco Lindor. A single by Brantley scored Kipnis, and then Napoli belted a towering three-run homer into the left field bleachers that extended the Indians? lead to 4-0.

Bauer pitched three scoreless and hitless innings to start the game, but then ran into trouble in the fourth when Nick Castellanos, who leads the league in hitting, ripped an opposite field three-run home run over the right field wall to cut the Cleveland lead to 4-3.

"Castellanos is hitting everyone now," Francona said.

"Nick's been the most consistent offensive player we have," Ausmus said.

The Indians got that run back in the bottom of the fourth when Gimenez, who was acquired in a trade with Texas on Tuesday, hit a two-out solo home run over the centerfield wall, Cleveland a 5-3 lead.

"They got right back in it, so it was nice for us to answer back like that," Francona said.

NOTES: Indians backup C Roberto Perez will undergo surgery on his right thumb Friday. No timetable has been set for his return. He injured the thumb in a home plate collision on April 30 in Philadelphia. ... Indians manager Terry Francona said DH Carlos Santana, who became the DH after losing his job at first base to 1B Mike Napoli, has begun to occasionally take fly balls in right field in pregame drills. ... Tigers SS Jose Iglesias, hitting .194 in his last 10 games, was given a day off Thursday. ... Tigers INF Andrew Romine started his first major league game in center field on Thursday. Romine has started two games at shortstop and one at first base this year.