DETROIT (AP) — On a night the Tampa Bay Rays needed a strong start to rest their bullpen and snap a five-game losing streak, David Price could only go five innings.

Good thing he made them all count.

Price struck out nine and set a team record with his 15th win, helping the Rays beat the Detroit Tigers 6-3 on Monday night.

The Rays' blossoming ace walked four batters and threw 115 pitches, but only gave up two runs before turning it over to the bullpen.

"I kept getting ahead of guys and then letting them crawl back into the count," Price said. "This was a night where I should have gone seven or eight innings, and I only gave us five."

The previous record of 14 wins was shared with James Shields (2008), Edwin Jackson (2008) and Rolando Arrojo (1998).

"It's a great honor to set a record like that — that's an awesome feeling," Price said. "I just have to make sure I don't leave it stuck on 15."

Matt Joyce homered to help the Rays send Detroit to its eighth loss in 10 games to stay nine behind Chicago in the AL Central.

Three Rays relievers finished, with Rafael Soriano pitching the ninth for his 32nd save in 34 tries. The four Tampa Bay pitchers combined for 13 strikeouts.

Chad Qualls replaced Price and pitched nearly two innings.

"Our bullpen was short tonight, and we knew it was going to be tough for us to piece together four innings," Maddon said. "If we didn't get five outs from Chad, we would have never done it. That might have been the biggest key to the game tonight."

Joaquin Benoit pitched the next 1 1-3 innings before Soriano took the ninth.

Armando Galarraga (3-5) allowed four runs in five innings. Galarraga has only won one of 11 starts since nearly throwing a perfect game on June 2.

"Galarraga had a bad night," Tigers manager Jim Leyland said. "He had no control of the strike zone."

Joyce, who broke up Max Scherzer's no-hit bid with a grand slam on July 26, led off the third with another homer against the Tigers.

Tampa Bay then scored twice on sacrifice flies, the first by Ben Zobrist later in the third and the next by Joyce in the fourth.

The teams traded runs in the fifth. Evan Longoria's RBI double gave the Rays a 4-1 lead in the top of the inning. Ryan Raburn hit a RBI single in the bottom half, but Price struck out the next three hitters, hitting 100 mph on his last pitch of the night.

"I knew that if I gave up one more runner, I was done, so I was just going after those guys with everything I had," Price said. "I didn't want to make us go to the 'pen even earlier than I did."

Brennan Boesch's 14th homer made it 4-3 off Joaquin Benoit in the eighth, but Jaso and Crawford singled home insurance runs in the top of the ninth.

In the first inning, Tigers left-fielder Jeff Frazier threw out John Jaso out after Carl Crawford's shallow fly ball. Detroit took advantage to go up 1-0 on Gerald Laird's RBI single in the second.

"We made Price work, we made him earn his innings and we got his pitch count up," Laird said. "I was happy with our approach. We just didn't get the job done."

NOTES: The Rays placed RHP Jeff Niemann (shoulder strain) on the 15-day disabled list before the game and called up reliever Mike Ekstrom from Triple-A Durham. After the game, they placed fellow starter RHP Wade Davis on the disabled list with the same injury and called up RHP Jeremy Hellickson, who will start in place of Davis on Tuesday. ... Ramon Santiago, who made his major-league debut in 2002, started at designated hitter for the first time in his career. He was the Tigers' 10th starting DH this season. ... Joyce's homer ended a 0 for 18 slump that included 10 strikeouts. ... In Longoria's first plate appearance since breaking up Brandon Morrow's no hitter Sunday with two out in the ninth, he faced Galarraga, the only other pitcher this season to lose a no-hit bid with two out in the ninth.