The right-hander issued just one walk and struck out nine in the 110-pitch gem, twirling his first shutout since 2009 as the Dodgers won for seventh time in nine games.
Second-place Los Angeles came into the contest trailing National League West-leading Arizona by 2 1/2 games.
The Dodgers scored the game's only run on an first-inning RBI groundout by Hanley Ramirez.
Tyler Chatwood (5-3) took the complete-game loss for Colorado, yielding just the one run on four hits over eight innings. He walked two and fanned four.
Celebrity Families of 2014 [PHOTOS]