Considered Detroit's top pitching prospect, Fulmer (1-0) allowed seven hits, walked one and struck out four.
Detroit got the 23-year-old righty last summer in the trade that sent slugger Yoenis Cespedes to the New York Mets. Last season's Eastern League Player of the Year, Fulmer was 1-1 with a 4.11 ERA and 20 strikeouts in 15 1/3 innings of Triple-A action before his Friday call-up.
Consistently reaching the mid-90s with his fastball and coupling it with a sharp slider, Fulmer struck out three of the first six Minnesota hitters.
He was cruising until three straight two-out singles in the fourth inning resulted in one Minnesota run. An RBI double by Miguel Sano pulled the Twins to 4-2 in the fifth.
For the second straight start, Phil Hughes (1-4) struggled to get the first three outs for Minnesota.
J.D. Martinez had an RBI double in the first inning as Detroit took a 3-0 lead. Hughes allowed two first-inning runs last Saturday in a 2-0 loss at Washington.
Hughes, who threw 27 pitches in the first, lasted a season-low five innings, allowing seven hits and four earned runs.
The last of those runs came off the bat Cabrera. A career .439 hitter against Hughes, the slugging Tiger homered in the fifth to make it 4-1. It was Cabrera's sixth career home run off the Minnesota right-hander, his most off any pitcher.
Victor Martinez and Castellanos hit solo shots in the eighth.
Tigers: OF Cameron Maybin (left wrist fracture) was to serve as designated hitter at Triple-A Toledo Friday as he continues his rehabilitation. ... C James McCann was to catch nine innings at Toledo Friday as he works his way back from a right-ankle sprain. Manager Brad Ausmus wouldn't rule out McCann returning to the Tigers this weekend.
Twins: RHP Ervin Santana on the 15-day DL since April 20 with a lower back strain is scheduled to have a light throwing session Saturday. ... Manager Paul Molitor indicated that RHP Kyle Gibson, on the DL since April 23 with a right shoulder strain, probably won't come off when he's eligible, but was optimistic Gibson wouldn't miss much more time than that.
Tigers: RHP Jordan Zimmermann (4-0, 0.35 ERA) starts Saturday in the middle game of the three-game series. He has allowed just one earned run in his four starts, including 24 1/3 scoreless innings to begin the year.
Twins: RHP Tyler Duffey (0-0, 2.25) pitched four innings last Sunday in Washington before exiting the game after getting hit on his throwing shoulder by a line drive.