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.
Celebrity Breakups and divorces of 2014 [PHOTOS]