Shane Greene allowed three runs and five hits in 2 2/3 innings for the Tigers. John Mayberry Jr., trying to earn an outfield job, hit his first homer of spring training, a tiebreaking drive in the seventh off Jacob Faria.
Non-roster player Kyle Roller homered for Tampa Bay.
Kinsler got his second double in two days and lifted his spring average to .333. He's one of several players competing for the leadoff spot.
"I feel fine, it's early in the spring," Kinsler said after playing five innings. "I'm just getting into the groove."
"There are a lot of possibilities," Ausmus said. "It is too early to tell."
Rays: Erasmo Ramirez gave up five runs and seven hits in two innings, raising his ERA to 11.25.
Tigers: Greene made his second start of the spring. He was shaky but unconcerned about the subpar results.
"I felt fine today, I am just trying to grip and get some outs," Greene said. "It feels fine."
Greene went 4-8 in 16 starts for the Tigers last season.
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