Zimmermann, who has been sidelined with neck issues, was touched for three runs on five hits in four innings. Alex Wilson came on to start the eighth inning against Joe Mauer, who lined a pitch off Wilson's right leg for a single.
Efren Navarro hit two solo home runs for Detroit.
Cabrera ended up leaving the game because of lower back tightness. The ball carried an exit velocity of 103.8 miles per hour and forced Wilson to leave the game with a non-displaced fracuture of his right fibula. He limped off the field with help and was replaced by Daniel Stumpf. That moved paid off when Eddie Rosario lined a single to left that the speedy Granite scored from second to tie the score at 3-3.
Reliever Joe Jimenez hit a batter and caught a line drive before giving up a two-run line single to center by Robbie Grossman, making it 6-3. Santana gave up hits to the Tigers' first four batters and the Twins quickly fell behind 2-1. The Twins got another run on a groundout to second by Jason Castro. Grossman then added a two-run single, and Granite eventually came up to deliver his three-run homer to make it an eight-run inning.
Granite, the 10th man to bat in the eighth, hit a three-run shot off Blaine Hardy for his first big-league homer. Kinsler's RBI single in the third put Detroit up 2-1.
Brian Dozier led off the game with a Little League home run, bunting to Jeimer Candelario and circling the bases when the third baseman's throw went into right field for a three-base error. Cabrera blooped a single near the line in right and Nicholas Castellanos plopped an RBI single into short left.
NOTES: Tigers OF Mikie Mahtook's return this season is doubtful after he was diagnosed with a Grade 2 left groin strain suffered Friday night, a recurrence of an injury that struck him earlier this month. The Twins counter with right-hander Ervin Santana, the likely choice to pitch a wild card playoff game should Minnesota be involved and if his team can clinch in time to set it up.