Juan Uribe's third hit -- half of the team's total -- came with one out in the ninth inning off LaTroy Hawkins and brought home Matt Kemp, who led off the inning with a walk on four pitches and took second on Scott Van Slyke's groundout.
Uribe's bullet went past second baseman DJ LeMahieu, whose vision was partially screened by umpire Pat Hoberg, Rockies manager Walt Weiss said.
"DJ got screened off the ball by the umpire who didn't see the ball. It happens," said Weiss. "The ball was hit hard and the umpire didn't have time to move and DJ didn't see the ball."
Greinke now is 11-4 with a 2.66 ERA and is tied for the Major League lead in victories. He's 7-0 against the NL West and 13-1 since joining the Dodgers. He struck out eight, walked two (one intentionally) and pitched out of a serious jam after the Rockies tied the game in the bottom of the eighth. Dodgers starters have not issued more than two walks in a record 37 consecutive games.
"All of my pitches were useable and I got ahead of the count with quality pitches," said Greinke. "I got a lot of first-pitch outs, five or six, and a couple double plays. That was key."
With Hanley Ramirez back in the lineup after calf and shoulder issues, the Dodgers won by out-executing the Rockies. Their first run was set up by Dee Gordon's bunt single, aided by Colorado's inability to turn a double play and driven in by Adrian Gonzalez's single, his 53rd RBI. Their second run was set up by Uribe's double, aided by a passed ball and scored on a sacrifice fly by A.J. Ellis.
"You've got to play clean games against the good clubs," Weiss said.
Kenley Jansen pitched the ninth inning for his 26th save, which ended with pinch-hitter Ryan Wheeler's fly ball to the warning track caught by Yasiel Puig.
Colorado scored a two-out run in the fifth with an assist from the Dodgers' defense. LeMahieu's gapper to right-center skipped off the glove of Puig for an error. LeMahieu then scored the unearned run on a pinch-hit double by Josh Rutledge.
The Rockies tied the game at 2 in the eighth. Charlie Blackmon led off with a single. Drew Stubbs popped out on a bunt attempt, but Justin Morneau tripled to right-center, scoring Blackmon.
"A bad pitch," said Greinke.
Manager Don Mattingly went to the mound, but left Greinke in to pitch to Troy Tulowitzki (.351) with first base open and Corey Dickerson (.337) on deck.
"We wanted to go after him [Tulowitzki] and get an out," said Mattingly.
Tulowitzki popped out to shallow left field.
"I think a lot of times a hitter knows you're pitching around him and I kind of wanted to throw a strike the first pitch and let him know I'm not pitching around you in that case," said Greinke.
The left-handed Dickerson was walked intentionally to bring up the right-handed Nolan Arenado, who was activated before the game after fracturing a finger. But Greinke struck him out with a 94-mph fastball.
As the Dodgers returned to their dugout for the ninth, Gonzalez exhorted his club to break the tie.
"I didn't hear what he was saying, but it felt like everyone was still excited about the game," said Greinke. "It felt like even though I gave up the run the last inning, we were just as confident as we were before."
"We hadn't done much offensively and I wanted to see if we could get something going, to get Zack a win, he pitched so good," said Gonzalez. "Any time you hold them to two runs in this place, it's special."
Uribe had his first multi-hit game since returning from the disabled list with a strained hamstring on June 26.