Two days after Price allowed eight runs in a 13-4 loss to the New York Yankees, it was Greene's turn. He gave up eight runs and nine hits in four-plus innings Friday night as the Cleveland Indians routed the Tigers 13-1.
Greene (3-1) had allowed only one earned run in 23 innings coming into the game, but Brandon Moss hit a two-run double off him in the first. It never got better, and Moss finished with two homers and seven RBIs.
"I felt really good, but I left some balls up and paid for it," Greene said. "These are the best hitters in the world, and you have to make your pitches."
Detroit has lost four straight after an 11-2 start.
"I don't know if I would call anything a trend at this point," Tigers manager Brad Ausmus. "We've had a lot of low-scoring games, and a few high-scoring games mixed in. Obviously, you're never happy with a game like this one."
Danny Salazar (2-0) gave up one run on six hits and three walks while setting a career high with 11 strikeouts in seven innings for Cleveland.
"I'm challenging guys now, and tonight I was able to throw all my pitches when I needed them," he said.
Salazar was handed a two-run lead in the first inning, thanks to Moss, but the Tigers loaded the bases in the bottom half with two outs. Yoenis Cespedes launched a drive to deep right-center, but Michael Bourn ran it down on the warning track.
"That's the play of the game right there," Indians manager Terry Francona said. "That's a grand slam in any other park other than maybe Houston, and if it gets down here, it is three runs. Instead, Michael gets us out of the inning, and Danny was great from there."
Moss followed up his first-inning double with a three-run homer in the fifth and a two-run shot in the ninth. He came into the game hitting .162 with two RBIs in 12 games.
"We knew Brandon was going to break out, and that was going to mean some big production," Francona said. "When he gets going, he can carry a team."
Lonnie Chisenhall hit a two-run homer in the eighth for the Indians, who entered with 11 homers — none with runners on base.
The Indians made it 3-0 in the second, but the Tigers got a run back on Nick Castellanos' homer in the bottom half.
Cleveland broke the game open in the fifth with a little help from Detroit's defense. With two on and none out, Jason Kipnis bunted down the third-base line. The ball briefly rolled foul, but Castellanos picked it up just as it came back onto the line.
Michael Brantley followed with an RBI single, and Carlos Santana made it 6-1 with a double that sailed over the head of J.D. Martinez in right. Moss then hit Alex Wilson's first pitch for a three-run homer.
David Murphy doubled on Al Alburquerque's first pitch in the eighth, and Chisenhall followed with a homer to right. Moss hit his second homer of the night off Alburquerque in the ninth.
Detroit: Ausmus said RHP Justin Verlander remains in limbo. Verlander, who hasn't pitched this season due a triceps strain, hasn't thrown since a simulated game had to be cut short by fatigue and soreness last week.
It was the 114th anniversary of the first game in American League history, which saw the Chicago White Stockings beat the Cleveland Blues 8-2 in 90 minutes. Every other AL game that day was rained out.
Indians: Trevor Bauer (2-0, 0.95 ERA) will start Saturday afternoon against the Tigers. Bauer, who has never lost to Detroit in five career starts, has not allowed a run in 13 innings on the road this season.
Tigers: Alfredo Simon (3-0, 1.74) will pitch in Saturday's Negro Leagues Tribute game. Simon is 2-2 with a 5.40 ERA in eight career appearances against the Indians, including three starts. Cleveland has scored more runs (20) against him than it has strikeouts (18).