Nicasio (8-6) scattered four hits and walked two in the 95-pitch effort, turning in his third straight start of allowing two or fewer runs.
Todd Helton smacked a two-run homer, Charlie Blackmon added a solo shot and Nelson Arenado went 3-for-4 with two runs scored as Colorado took the opener of a three-game set.
Giants starter Barry Zito (4-10) was tagged for five runs on nine hits over four full innings.
Joaquin Arias provided San Francisco's only RBI.
Notable deaths of 2014 [PHOTOS]