The Rockies scratched out three runs over the first five innings and the lead stood up thanks to the work of Nicasio, Rex Brothers and Rafael Betancourt.
Nicasio (5-4) allowed three of the Los Angeles hits and struck out three while throwing 101 pitches. Brothers walked a batter in the eighth and Betancourt worked around a leadoff single in the ninth for his 14th save.
Troy Tulowitzki had a sacrifice fly in the first and Wilin Rosario drove in a run with a single later in the inning. D.J. LeMahieu had an RBI base hit in the fifth.
Those three runs were charged to Clayton Kershaw (8-6), who struck out 10 and allowed six hits over seven innings.