Greinke (2-0) allowed three runs and five hits in 6 2-3 innings, improving to 20-1 with a 1.95 ERA in 30 starts against NL West teams since signing with the Dodgers in December 2012.
Joel Peralta pitched a hitless ninth for his third save in as many chances.
Gonzalez, who led the majors last season with 116 RBIs, has 14 in his first 11 games and is batting .523 (23 for 44).
Jordan Lyles (1-1) gave up four runs, five hits and five walks in six innings, dropping to 0-3 with a 6.84 ERA in four starts against the Dodgers.
Lyles walked three of his first four batters in the fifth, including Yasiel Puig, who stared down the Lyles after a belt-high wild pitch that just missed hitting the batter. Puig sat out the previous three games because of tightness in his left hamstring.
Troy Tulowitzki's run-scoring single put Colorado ahead in the first, but Yasmani Grandal's RBI single tied the score in the second.
After the Dodgers loaded the bases with one out in the third, Gonzalez hit what appeared to be a double-play grounder to Tulowitzki at shortstop. But second baseman DJ LeMahieu's relay throw in the dirt couldn't be handled by first baseman Justin Morneau, and Greinke scored the go-ahead run.
Gonzalez made it 4-1 in the fifth with a two-run, opposite-field double to left-center that Blackmon missed on a diving attempt in the warning track.
LeMahieu's two-run homer in the seventh, on Greinke's 103rd and final pitch, ended the LeMahieu's 52 at-bats homerless streak at Dodger Stadium. Puig and Howie Kendrick had RBI doubles in the bottom half against Brooks Brown.
Greinke, who threw a career-high 12 wild pitches last season, made two in a row in the third inning.
Dodgers: LF Carl Crawford did not play because of a stomach ailment and was replaced by Andre Ethier, who started the previous three games in RF while Puig was sidelined. Ethier had not started in four consecutive games since June 28-July 2 last year. ... Closer Kenley Jansen threw off a mound for the first time since left foot surgery in February. His bullpen session lasted 15 pitches.
Rockies: RHP Eddie Butler will make his sixth career start and third against the Dodgers, the team he made his big league debut against last June 6 at Coors Field. Last Monday, he pitched 5 1-3 scoreless innings despite giving up six walks.
Dodgers: RHP Brandon McCarthy surrendered four home runs while striking out 10 and walking none in a seven-inning no-decision last Monday against Seattle at Dodger Stadium. The 10-year veteran, who played high school ball in Colorado Springs, is 0-2 with a 6.75 ERA in four career starts against the Rockies.