The Marlins, who had the worst record in the majors last week, extended the longest active winning streak in the big leagues.
The Tigers wrapped up an 0-9 stay at Comerica Park against Houston, Oakland and the Marlins. That record doesn't include a suspended game in which Detroit trails Oakland in the late innings.
Miami benefited from a couple of fielding lapses by the Tigers in the ninth to come back against Shane Greene (0-2), who had been 15 for 15 on save chances this season.
It was 2-0 when Harold Ramirez opened the inning with a grounder that third baseman Dawel Lugo misplayed for an error. Ramirez later scored on Neil Walker's single.
Greene later induced a double-play ball to second baseman Ronny Rodriguez that would've ended the game. But Rodriguez bobbled it and Miguel Rojas was called safe at first, which was held up on replay.
After an intentional walk to pinch-hitter Curtis Granderson loaded the bases, Cooper homered to deep left field. On Wednesday, Cooper hit his first career home run in a 6-3 win.
Marlins starter Trevor Richards struck out six over 5 2/3 innings, allowing eight hits and one run.
Tyler Kinley (1-0) gave up one run in the eighth and got the win. Sergio Romo earned his ninth save with a perfect ninth.
For Detroit, right-hander Matthew Boyd threw six scoreless innings and Miguel Cabrera continued moving up the all-time lists in the loss.
Cabrera had an RBI single in the eighth. It was his second hit of the game and moved Cabrera into 60th place on baseball's career hit list with 2,727, one more than Chipper Jones.
With the bases loaded in the sixth inning, Rodriguez hit a flyball to left field. Austin Dean made a sliding catch on the sacrifice fly for a 1-0 lead.
Cabrera went into the game tied with Carlos Beltran for 61st on the hits list.
Marlins: Coming off the best start of his career, RHP Pablo Lopez (3-5, 5.06) will start Friday at Washington and RHP Kyle McGowin (0-0, 6.00).
Tigers: Rookie LHP Gregory Soto (0-2, 10.80) opens a three-game series and nine-game road trip Friday at the Mets, who are throwing RHP Noah Syndergaard (3-4, 4.50).
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