The Rockies were trailing 3-1 in the sixth when they scored five times to grab control of the contest, whose start was delayed 1 hour, 48 minutes by rain.
Michael Cuddyer began the rally with a leadoff single against Pirates starter A.J. Burnett. After Todd Helton struck out, Cuddyer went to second on Wilin Rosario's fly-out and scored on a Nelson Arenado double.
Jonathan Herrera then drew a walk and pinch-hitter Charlie Blackmon delivered another run-scoring two-bagger, forging a 3-3 tie.
That brought up Fowler, who lined a single to right, scoring Herrera and Blackmon with the go-ahead runs.
Wilton Lopez (2-4) recorded the final out in the sixth to notch the victory and Rex Brothers picked up his ninth save despite yielding a run in the ninth.
Burnett (5-8) ended up yielding six runs (five earned) on eight hits over 5 2/3 innings.