Pacheco put the Rockies up 3-0 with his first-inning homer and LeMahieu made it 5-1 Colorado with his second-inning shot.
Chris Nelson and Matt McBride each drove in a run for the Rockies, who won their fourth straight after a nine-game losing streak.
Jhoulys Chacin (3-5) went five innings, giving up three runs on seven hits with four walks and two strikeouts, to get the victory.
Cubs' starter Chris Volstad (3-11) allowed seven runs on 10 hits in three innings.
Anthony Rizzo hit a solo home run in the third and drove in a run in the ninth, when the Cubs scored twice to cut the lead to two. Rafael Betancourt then set down the next three batters and collected his 31st save.