The Dodgers have now beaten the D-backs eight of the nine times the teams have played this year. Throw out their games against Arizona, and the Dodgers would be a pedestrian 15-19.
"We've got to figure something out, because obviously it's not fun getting beat by those guys over and over at our place on our home field," D-backs starter Wade Miley said. "We've got to make some adjustments."
Yasiel Puig got the Dodgers' offense started in the third inning with a one-out homer off Miley for a 1-0 lead.
"I had gone down and away the pitch before and I was trying to go right back there and overthrew it a little bit and up and middle," Miley said. "Bad pitch."
The Dodgers added a pair of runs in the second when A.J. Ellis singled home a run and Greinke helped himself out with an RBI double.
"I kind of had a chance to get out of it," Miley said. "Had Greinke 1-2 and tried to go in and he did a good job of extending the inning. That hurt a little bit, giving up a double to the pitcher."
Meanwhile, the D-backs were not able to capitalize on some early opportunities against Greinke.
"He was outstanding tonight," D-backs outfielder A.J. Pollock said. "He's got a ton of pitches going for him and he's able to not just throw them for strikes, but throw them for strikes on the corners. It's tough to hit."
Their best chance came in the second, when Aaron Hill led off with a single and Pollock followed with a walk.
The rally died quickly when Chris Owings, bunting for a hit, popped up to third base and Ender Inciarte grounded into an inning-ending double play.
After allowing a hit in each of the first three innings, Greinke found his groove and retired 10 straight until Paul Goldschmidt's two-out walk in the sixth.
"I don't care how hot a pitcher is, you always want to try and make him uncomfortable, and I don't think we did a good job at all of making him uncomfortable," Pollock said. "There's guys that go out there and it's their day, but a good offensive club tries to find ways to make him throw a couple more pitches, make him get his pitch count up. I think we could have done a better job of that."
Greinke allowed two runs or fewer for his 21st straight start as he improved to 7-1, becoming the National League's first seven-game winner.
"Greinke just had a great feel for all his pitches," Gibson said. "Threw his fastball, his slider, his curveball, his change, pounded the ball down, pounded on both sides of the plate where he wanted to, kept us off balance, and we weren't able to match that."
Scott Van Slyke continued his ownership of Miley with a solo homer in the sixth. Van Slyke is now 6-for-9 with three doubles and three homers against the left-hander this season.
"It makes the at-bat easier," Van Slyke said of knowing he's had success against Miley. "You're not anxious what pitch is coming, you don't have to figure out what he's trying to do. Just go up and look for something to whack. I got a 2-1 change and reached for it, kind of lucky [the double]. The home run was a fastball up and I got it good. Certain guys you just pick up the ball early. His rhythm and my rhythm are synced up. Some guys you just feel comfortable against."
Miley (3-4) is clearly frustrated by his inability to make pitches against Van Slyke.
"It's getting ridiculous," Miley said. "One thing I can say is he's onto me right now, but I'm not making good pitches to him at all. There's guys that own you where you make good pitches and they hit you. Mark Ellis owns me as far as that goes, I make good pitches to him he still gets hits. I'm just not making good pitches to Van Slyke. The pitches he's hitting, he's supposed to hit them, like fastballs right down the middle."