McCutchen, who leads the majors in hitting, led off the fourth with his 22nd homer of the season to tie the score 1-1.
Drew Sutton drove in the eventual game-winner with a single in the fifth inning and came around to score on a wild pitch by Christian Friedrich (5-7). Neil Walker went 2-for-3 to extend his hitting streak to 17 games.
Friedrich took the loss after giving up five runs on six hits in 4 2/3 innings. He allowed four runs in the fifth.
Erik Bedard (5-10) notched his first win since June 8, allowing one run on eight hits over 6 2/3 innings.
Josh Rutledge had an RBI triple for the Rockies, who have lost three of their last four games.