CLEVELAND -- The Detroit Tigers only had one big inning Tuesday night, but that was easily enough to win the game.

Yoenis Cespedes and Nick Castellanos had the big hits in a six-run fifth inning while David Price continued his domination of the Cleveland Indians as the Tigers won 7-3 Tuesday night at Progressive Field.

Price (7-2) pitched 6 2/3 innings, throwing 114 pitches and allowing one run on nine hits with seven strikeouts and no walks.

"David battled quite a bit, but he still did an excellent job," Detroit manager Brad Ausmus said.

With the win Detroit is now 9-2 against Cleveland this season. Since the start of the 2013 season the Tigers are 35-14 versus the Indians, and Detroit has won 16 of the last 19 meetings. The slumping Indians have an American League-worst home record of 14-23.

This game was close for four innings, but the Tigers blew open a 1-1 game in the fifth, with all of the runs coming against right-hander Danny Salazar (6-3). Left fielder Cespedes and third baseman Castellanos both belted two-run doubles in that rally.

In his three starts against Cleveland this season Price is 2-0 with a 0.42 ERA, having allowed one run in 21 1/3 innings, with 21 strikeouts and three walks. In 12 career starts against the Indians, Price is 9-1 with a 2.04 ERA.

"I don't worry about the opponent. I just try to go out there and pitch my game," Price said.

Shortstop Andrew Romine homered and had two hits for Detroit, while first baseman Miguel Cabrera and designated hitter Victor Martinez also had two hits apiece.

Trailing 7-1, Cleveland scored two runs in the ninth inning off right-hander Josh Wilson, with one of the runs coming on an RBI double by second baseman Jason Kipnis, who had four hits while extending his hitting streak to 18 games.

Besides the career-high 18-game hitting streak, Kipnis also has a 27-game home hitting streak, the longest home hitting streak by an Indians player since Miguel Dilone hit in 27 consecutive home games in 1980.

Detroit took a 1-0 lead when Romine led off the top of the third inning with a home run over the right field wall.

Cleveland tied it in the bottom of the third on a sacrifice fly by shortstop Francisco Lindor.

Detroit's big fifth inning was aided by a Salazar error. Romine led off with a double, and the next two batters, right fielder Rajai Davis and second baseman Ian Kinsler, drew walks, loading the bases with one out.

Cabrera hit a dribbler back to the mound. Salazar fielded it, but dropped it as he attempted to throw home to start what could have been an inning-ending double play. Instead, the error allowed Romine to score, giving Detroit a 2-1 lead before the onslaught continued.

"Salazar is a very tough pitcher with a bright future," Ausmus said. "But we were fortunate to be able to put some runs on the board after he made that mistake."

"When you get Miggy to hit one 15 feet, and you think you might get a double play, but don't get anything -- that's tough," said Cleveland manager Terry Francona.

Salazar fielded the ball cleanly, but it slipped out of his hand as he began to make the throw home.

"When he hit it to me, I was thinking double play, but I tried to be too quick, instead of making sure I got one out. I lost the ball, and gave the game away," Salazar said.

Martinez followed with an RBI single, and Cespedes also singled, scoring Kinsler and Cabrera to make it 5-1.

Salazar was relieved by right-hander Zach McAllister following Cespedes' hit. In 4 1/3 innings, Salazar (6-3) gave up seven runs, six earned, on six hits with eight strikeouts and three walks.

Castellanos hit McAllister's first pitch into the right-field corner for a double, scoring Martinez and Cespedes, and giving the Tigers had a 7-1 lead.

During Cabrera's at bat in the fifth inning Cleveland pitching coach Mickey Callaway visited the mound. On his way back to the dugout he got into an argument with home plate umpires Eric Cooper, who ejected Callaway from the game.

"We thought Price was getting some pitches that Danny wasn't getting," Francona said.

NOTES: RHP Scott Atchison was designated for assignment by the Indians. His roster spot was taken by RHP Austin Adams, who was recalled from Triple-A Columbus. ... 2B Jason Kipnis had 94 hits in the Indians' first 69 games. That's the most hits in the team's first 69 games since Carlos Baerga had 96 in the first 69 games in 1995. Kipnis added four hitsTuesday. ... Tigers OF J.D. Martinez was not in the lineup Tuesday, mostly because of his poor career numbers against Indians RHP Danny Salazar. Martinez had a career average of .111 (1-for-9) with seven strikeouts against Salazar.