Carlos Gonzalez smashed a two-run shot in the fifth to erase a 4-2 deficit and the Rockies scored three more runs in the seventh to grab the lead, triggered when Tulowitzki drove in Dexter Fowler with sacrifice fly.
Cuddyer finished 3-for-5 and Rafael Betancourt collected a save for Colorado, which rebounded from a season-opening 5-4 loss at Milwaukee and notched its first win under new Manager Walt Weiss.
The Brewers' Michael Gonzalez (0-1) was tagged for three runs after issuing two hits and a walk in the seventh.
Ryan Braun cracked a two-run homer for Milwaukee.
Celebrity Breakups and divorces of 2014 [PHOTOS]