Greene went 1-for-4 with a walk and a solo home run in Tuesday's 8-0 win over the Rays.
Greene has now gone deep on consecutive days to begin June, and he's up to six home runs this season across 62 games to go along with a strong .859 OPS. He has a lot of work to do if he wants to match his regular-season total of 36 homers from last year, but the 25-year-old is off to a great start this month, and he should remain locked into fantasy lineups as Detroit's primary offensive catalyst.