The Brewers had grabbed a 5-4 lead in the top of the eighth on a two-run homer by Yuniesky Betancourt, but the Rockies responded quickly in the next half-inning.
After Todd Helton flew out, Cuddyer advanced to third on a wild pitch and Arenado made Axford pay by lining a solid hit to center field for the decisive run.
Cuddyer, Tulowitzki, Dexter Fowler and Corey Dickerson each went 2-for-4 with a solo homer as Colorado took the rubber match of a three-game series.
Matt Belisle (5-5) was credited with the decision despite yielding Betancourt's homer and Rex Brothers tossed a 1-2-3 ninth for his seventh save.
Norichika Aoki also went deep and Jeff Bianchi supplied a pair of run-scoring singles for the Brewers.