Pacheco doubled off Clippard (2-3) to start the frame and went to third on Jonathan Herrera's sacrifice bunt.
With pinch-hitter Jason Giambi at the plate, Clippard uncorked a wild pitch, allowing Pacheco to scamper home with the decisive tally.
The Rockies also scored the tying run on a Michael Gonzalez wild pitch in eighth, capping a rally that began with a pinch-hit, solo homer by Eric Young off Sean Burnett.
Rex Brothers (4-2) earned the win with a scoreless eighth inning and Rafael Betancourt notched his 16th save for the Rockies, who took the rubber match of a three-game series.
Ian Desmond went 2-for-4 with a two-run homer for National League East-leading Washington.