The right-hander, though, might have a challenge as he attempts to improve to 5-0 on Wednesday night because he'll face one of the most prolific run-scoring teams in the majors and one of the most patient, the Minnesota Twins.
The Dodgers (14-12) won two of three over Arizona to kick off their 10-game stay at home but dropped five of the final seven. They played without Hanley Ramirez (bruised right thumb) in a 6-1 loss to Colorado on Sunday after he was forced to leave the previous game and were denied their 10,000th all-time win.
Ramirez is hoping to return for this series, but it's unknown if he'll be back in the lineup in time to help Greinke (4-0, 2.45 ERA). Greinke struck out a season-high 11 over seven-plus innings in a 5-2 victory against Philadelphia last Wednesday.
He has allowed two runs or fewer and pitched at least five innings in 20 consecutive starts, including three in the postseason, dating to July 30.
"What I really try to do is try not to have a bad game, and it's been working for a while," Greinke told the team's official website.
Greinke will next try to deny the Twins their fifth victory in seven games and seventh in the last nine at home.
Minnesota (12-11) has scored 37 runs and posted a .369 on-base percentage during its past six games. The Twins have needed all of that production to overcome their inconsistent pitching.
Minnesota allowed 34 runs in that span, and its 5.00 ERA is one of the worst in the majors.
The Twins have stayed above .500 by scoring 127 runs, mainly because of their discipline at the plate. While its .251 batting average and .389 slugging percentage are middle of the road, Minnesota has drawn 121 walks and owns one of the best on-base percentages in the majors at .353.
The Twins forced eight walks in a 5-3 win over Detroit on Saturday.
"I think everybody is just trying to get on base, and there's always conversation about it," manager Ron Gardenhire told the team's website. "A lot of our hitters have a few more at-bats in this league and understand it a bit more. It's experience and not panicking in certain situations."
Kyle Gibson (3-1, 3.63) was helping keep Minnesota's ERA down until a 7-3 loss in Tampa Bay last Tuesday. After posting a 0.93 ERA in his first three starts, the right-hander was tagged for seven runs and 10 hits over three-plus innings.
Gibson was originally scheduled to pitch Sunday's series finale against Detroit but that game was postponed due to rain. The opener of this series Tuesday was also postponed because of inclement weather and will be made up Thursday as part of a day-night doubleheader.
''They feel like they haven't been out there in a year, and it's only been a few days,'' Gardenhire said, adding: ''Mother Nature's winning right now.'' Gibson will be making his second career interleague start and first against the Dodgers.
Greinke has plenty of experience against Minnesota thanks to his time with Kansas City, but he hasn't faced the Twins since June 17, 2012.
He's 3-8 with a 4.74 ERA in 18 starts against his former AL Central rivals and 1-4 with a 6.10 ERA in the last eight.
The Dodgers are 3-6 against Minnesota since interleague play began and dropped two of three in their only visit to Target Field from June 27-29, 2011.
Trevor Plouffe, whose .310 average is best among Twins regulars, is expected to return from a bruised left triceps.