Cuddyer stroked a pair of run-scoring doubles and added a seventh-inning, fence-clearing shot, raising his average to .328, third-best in the National League.
D.J. LeMahieu's two-run double in the fifth broke a 2-2 tie for Colorado, which took the rubber match of a three-game series.
Corey Dickerson went 3-for-4 with two runs scored and Nelson Arenado added a solo shot for the winners.
Adam Ottavino (1-2) notched the win after starter Tyler Chatwood left in the third inning with a bruised thumb.
Reds starter Mike Leake (11-6) was lit up for six runs on eight hits in a 4 1/3-inning effort.
Shin-Soo Choo belted a two-run homer for Cincinnati, which holds a six-game lead over Arizona for a National League wild card berth.