With the scored tied 7-7 in the eighth, pinch-hitter Jason Giambi drew a two-out walk. Pinch-runner Jeremy Guthrie went to second on Dexter Fowler's single and both runners moved up on shortstop Jed Lowrie's fielding error.
That set the stage for Pacheco, who blooped a two-run single into center field off Fernando Rodriguez (1-5) to chase home the decisive runs.
The Rockies third baseman also delivered an RBI triple as Colorado pounded out 14 hits in the victory to begin four-game series.
Troy Tulowitzki went 3-for-4 with a solo homer and two RBI while Wilin Rosario provided two hits, including a two-run shot for the Rockies.
Lowrie hit a solo homer and drove in two runs for Houston.