Nicasio (9-9) scattered three hits over 5 1/3 scoreless innings, walking one and striking out seven.
Josh Outman, Adam Ottavino, Matt Belisle and Chad Bettis combined for 1 1/3 shutout relief innings, and Rex Brothers recorded the final four outs for his 18th save as the Rockies bounced back from an 11-0 thrashing in Friday's opener of a season-ending three-game series.
Nelson Arenado provided the contest's only RBI with a fourth-inning double.
Zack Greinke (15-4) tuned up for the playoffs with six innings of one-run ball, allowing four hits with no walks and seven strikeouts over six innings for the National League West champion Dodgers.
Disney's 'Jessie' to feature network's first engagement
Chipotle plans first price increase in 3 years