CLEVELAND -- After losing five of their previous seven games, the Detroit Tigers finished a bumpy first half of the season on a positive note.

Michael Fulmer pitched into the seventh inning, and Jose Iglesias had three hits as the Tigers beat the Cleveland Indians 5-3 on Sunday night at Progressive Field.

Fulmer (9-6) gave up three runs, two earned, on seven hits with one strikeout and one walk in six-plus innings. Justin Wilson got the last five outs to pick up his 10th save.

Cleveland's Nick Goody (1-1), in relief of starter Corey Kluber, gave up three runs in one-third of an inning to take the loss.

The Tigers were outscored 15-2 while losing the first two games of the series.

"We salvaged a win, and now we can go into the break not feeling sour about the way the games have gone," Detroit manager Brad Ausmus said. "We'll have a nice four days off and be ready to go for the second half."

For that, they can thank Fulmer, who outpitched Kluber in a battle of aces.

"I knew I had to put up zeros, and the offense did a great job of getting Kluber out after the fifth inning," Fulmer said.

Kluber was removed after five mostly because his pitch count was at 101. He gave up one run on three hits with eight strikeouts and three walks.

"He had to work so hard in the top of the fifth," Cleveland acting manager Brad Mills said. "He threw like 30 pitches and had traffic all over the place."

Kluber added, "They put together some good at-bats, and I didn't have my best command."

Goody came in to start the sixth inning with the score tied at 1-1. Miguel Cabrera led off with a walk and was forced out at second on a groundball hit by J.D. Martinez. Victor Martinez singled, moving the runner to second, and Nicholas Castellanos walked to load the bases.

Dan Otero relieved Goody, and Alex Presley greeted Otero with a double to left field, scoring J.D. Martinez and Victor Martinez, giving Detroit a 3-1 lead. Castellanos went to third on Presley's hit, then scored on an infield single by Iglesias to make it 4-1.

An RBI single by Castellanos in the seventh stretched the lead to 5-1.

Fulmer held Cleveland to one run on three hits through six innings before struggling in the seventh. Edwin Encarnacion led off with a single, and he rode home on Jose Ramirez's 17th home run, a shot into the right field seats on a 3-2 pitch that cut Cleveland's deficit to 5-3.

"I don't think I could have thrown a better pitch in that situation," Fulmer said. "A front-door sinker, down and in. There's a reason Jose Ramirez is starting in the All-Star Game."

Fulmer gave up singles to the next two batters and was removed from the game.

"I think the last two innings, there was a lot of down time (while the Tigers were hitting), and I think that got to him," Ausmus said.

Shane Greene escaped the inning, then got the first out in the eighth before Wilson entered. Wilson pitched out of a bases-loaded jam in the eighth, and then with a runner at first and two outs in the ninth, he struck out Francisco Lindor to end the game.

"It was certainly a well-earned save," Ausmus said.

Kluber retired the first eight batters he faced before giving up a two-out double to Iglesias in the third inning. Ian Kinsler followed with a soft single to center field on an 0-2 pitch to score Iglesias with the first run of the game.

The Indians scored an unearned run in the fourth inning to tie it. Bradley Zimmer led off with a single. Fulmer threw wildly to first on a pickoff attempt, allowing Zimmer to advance to second.

Fulmer retired Lindor on a flyout and Michael Brantley on a groundout, but Encarnacion doubled down the left field line, scoring Zimmer.

NOTES: Indians OF Lonnie Chisenhall left in the fourth inning due to a right calf strain. ... Cleveland 2B Jason Kipnis was placed on the 10-day disabled list with a right hamstring strain. To replace Kipnis on the roster, the Indians recalled 3B Giovanny Urshela from Triple-A Columbus. ... Tigers 1B Miguel Cabrera was 0-for-1 against RHP Corey Kluber, but Cabrera's career batting average against Kluber is still .434 (23-for-53) with three doubles, six home runs and 12 RBIs. ... Detroit RHP Shane Greene has inherited 34 baserunners, and only four have scored. He entered with two on and no outs in the seventh inning Sunday and didn't let a runner come home. Greene's 12.5 percent inherited-runners-scored percentage leads the American League.