The Reds tied the contest in the top of the seventh on a two-run blast by Brandon Phillips, his second of the game, but McCutchen came through with a leadoff shot of his own in the bottom half.
McCutchen also singled in two runs in the second in what was Pittsburgh's third win in four games.
Tony Watson (1-0) was credited with the win in relief despite allowing the homer to Phillips in the seventh. Jason Grilli worked out of a ninth-inning jam to collect his fourth save.
Cincinnati lost its third straight. J.J. Hoover (0-1) gave up the winning home run and retired just one batter during his brief stay in the seventh.
2014: The Year in Music [PHOTOS]