Haren struck out two and only experienced trouble in the third, when he allowed singles to James McCann and Andrew Romine to open the inning. He worked out of the jam thanks in large part to Dee Gordon's smooth turn of a double play at second.
"The results were good," said Haren, who hasn't allowed a run in his last two outings. "My stuff was moving pretty good. I wasn't quite as sharp as last game."
Haren threw 38 of his 58 pitches for strikes on a warm, muggy afternoon that saw the temperature climb into the mid 80s.
"I'm sure I'll be a little sore tomorrow, but that's the only way you can get in game shape," Haren said.
Ozuna homered off Alfredo Simon in the fourth.
Dee Gordon stole two bases, each one leading to a run. Giancarlo Stanton had a sacrifice fly and an RBI single.
Simon hadn't allowed an earned run in his first two spring starts before Miami touched him for three. He allowed three hits, a walk and hit a batter while throwing 53 pitches over four innings.
"I'm getting close to 100 percent," Simon said. "I need a couple more starts to throw all my pitches, then everything will be great."
J.D. Martinez hit his third home run of the spring in the sixth, a two-run shot for Detroit.
Marlins: With Miami off tomorrow, Henderson Alvarez will throw a simulated game against minor leaguers in the place of what would have been his scheduled turn in the rotation.
Tigers: David Price will make his third start of the spring when Detroit faces St. Louis in Jupiter.
Marlins: Pitcher Jose Fernandez threw a 35-pitch bullpen session on a back mound at the Marlins spring training complex on Sunday. Fernandez is working his way back from elbow-ligament replacement surgery.
Tigers: Manager Brad Ausmus said outfielder Yoenis Cespedes (quad tightness) might be ready to play in Monday's game. Slugger Miguel Cabrera will take batting practice prior to that game against the Cardinals but will not play in the game. For Cabrera, who underwent offseason ankle surgery and has yet to appear in an exhibition game, it will be the first time he takes batting practice on the road this spring. ... Alex Avila (back) will catch Monday.
Miami optioned pitchers Jose Urena and Kendry Flores to the minor leagues. Marlins manager Mike Redmond believes Urena is close to being Major League ready. "He's got a big league fastball. I think you saw that in the way he pitched the game he got in," Redmond said. The Marlins also reassigned pitchers Nick Wittgren and Trevor Williams, infielder Avery Romero, and outfielders Austin Wates and Kenny Wilson to minor league camp.
Marlins: Off Monday. On Tuesday the Marlins will start Jarrod Cosart against St. Louis.
Tigers: Remains in Jupiter overnight and will face St. Louis, who shares a complex with Miami. The Cardinals send John Lackey to the mound for the first time this spring.
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