CLEVELAND -- The way Cleveland Indians manager Terry Francona figures it, a poor defensive first inning cost his ace the ability to pitch the eighth, and that's when the game was decided.

Brian Dozier's home run leading off the eighth inning broke a tie, and Chris Gimenez added a solo shot in the ninth as the Minnesota Twins beat Cleveland 4-2 on Saturday at Progressive Field.

Dozier's homer, his 13th, came on a 3-2 pitch from Cleveland closer Cody Allen (0-3). Gimenez's homer, his fourth, came off Zach McAllister.

Taylor Rogers (4-1) pitched 1 1/3 scoreless innings to get the win. Brandon Kintzler pitched a scoreless ninth for his 20th save.

Cleveland starter Corey Kluber was sensational, striking out 13 in seven innings, allowing two unearned runs, three hits and two walks. Kluber has not allowed an earned run in his last 21 innings.

The two unearned runs Kluber allowed came in the first inning, thanks to two Indians errors. Dozier hit Kluber's first pitch of the game on the ground to second baseman Jason Kipnis, who threw wildly to first for an error. Joe Mauer walked, and Robbie Grossman doubled down the right-field line, scoring Dozier and sending Mauer to third.

Mauer then scored on a wild pickoff throw to third by catcher Yan Gomes, giving Minnesota a 2-0 lead.

"We took advantage of their mistakes right out of the chute," Twins manager Paul Molitor said.

"That was a shame," said Francona of the first inning. "They not only got two runs, but it probably cost (Kluber) pitching the eighth inning. The runs were important, but that cost him an inning."

Kluber was removed from the game after seven innings and 106 pitches.

"I was kind of disappointed in the way I handled the next two batters after the error," Kluber said.

The Twins were grateful for the two gift runs.

"You know it's going to be a battle anytime Kluber is out there," Twins starter Kyle Gibson said. "To get that 2-0 lead was huge because you never know when you are going to get runs off Kluber."

Gibson held Cleveland scoreless on one hit through the first three innings. But with one out in the fourth, Jose Ramirez drove a 3-2 pitch over the right field wall for his 12th home run, cutting the Twins' lead to 2-1.

After the first inning Kluber started striking out hitters in bunches. In one stretch in the middle innings, he struck out nine of 12 batters.

"Kluber was ridiculous. I think he struck out 38 guys," Gimenez joked. "He has a wipeout breaking ball that he throws harder than I throw my fastball."

Dozier's tiebreaking homer in the eighth inning came after the Indians scored a run in the seventh inning to tie the game at 2.

Gomes led off with a single against reliever Matt Belisle. Bradley Zimmer flied out for the first out, but Austin Jackson singled to left, moving Gomes to second.

Francisco Lindor hit a ground ball to first baseman Kennys Vargas, who threw to shortstop Jorge Polanco at second for the force on Jackson. But Polanco's return throw to first was wild, allowing Gomes to score the tying run.

"There wasn't much chance of completing that double play, so I would have rather we held the ball there, and kept the guy at third," Molitor said.

Rogers relieved Belisle and gave up an infield single to shortstop by Kipnis, with Lindor moving to second. But Rogers retired Ramirez on a groundout to end the inning.

"Rogers got some big outs at a big time in the game against some good hitters," Molitor said.

Gibson pitched 4 2/3 innings, giving up one run on four hits, with one strikeout and four walks.

NOTES: Twins 3B Miguel Sano sat out his second consecutive game because of a sinus infection. ... Twins OF Max Kepler was a late scratch from the lineup because of a bruised right foot, the result of a foul ball in Friday night's game. ... The visiting team has won 11 of the first 12 meetings this year. ... Indians C Yan Gomes has thrown out a major league-best 47 percent of attempted base stealers (15-of-32). ... Indians RHP Josh Tomlin will make his third start of the season against the Twins on Sunday. Tomlin was 1-1 with a 2.57 ERA in the first two starts. In his career versus Minnesota, Tomlin is 5-5 with a 5.13 ERA.