The Rockies ended an eight-game losing streak in emphatic fashion, sending 11 men to the plate in the 10th while hammering Jose Valverde (3-2). Four of the runs in the 10th were unearned due to a throwing error by Valverde.
Wilin Rosario singled in the first two runs of the inning and the outburst was eventually concluded by a three-run homer from Gonzalez and a solo shot by Cuddyer.
Chris Nelson also had three RBI for Colorado, two of them coming on a fourth-inning homer.
The huge 10th inning made a winner out of Matt Belisle, who threw two scoreless innings in relief.
Detroit had won four of its previous five.