Greinke is winless since beating San Francisco back on July 25 and is coming off back-to-back defeats by the Los Angeles Angels and most recently Milwaukee last Saturday. The Brewers reached Greinke for four runs and eight hits in six innings of that one to drop him to 12-8 on the year to go along with a 2.84 ERA.
The right-handed Greinke, who made 49 starts for Milwaukee from 2011-12, is 0-2 with an 8.10 ERA in two career starts against the Brewers.
Los Angeles won for the fourth time in five games on Thursday, as Dee Gordon had three hits and scored four runs to lead the Dodgers over the Atlanta Braves, 6-4.
Drew Butera added a two-run homer and Yasiel Puig had three hits and an RBI for NL West-leading Los Angeles, which has won seven of its last 10 and is the first National League team to 70 wins this season.
Dodgers starting pitcher Roberto Hernandez (7-8) got the win in his second start with the Dodgers since being acquired from the Philadelphia Phillies. The right-hander was charged with one run on three hits, striking out five and walking four in six innings.
"I feel better now," said Dodgers manager Don Mattingly. "If you lose today, you lose a half game. I like how we were able to come in here and take three out of four."
Milwaukee, meanwhile got a tremendous effort from starter Mike Fiers on Thursday and Scooter Gennett drove in two runs in the Brewers' 6-2 takedown of the Chicago Cubs. Khris Davis and Mark Reynolds both homered for Milwaukee, which halted a two-game skid.
Fiers (2-1) struck out a career-high 14 batters and allowed just three hits, a walk and no runs to win his second straight start. His 14 K's are the most ever thrown by a Brewer in a road game and second-most in franchise history. Ben Sheets fanned 18 batters for the Brewers in 2004.
"Just getting the win is awesome after losing the last two," said Fiers. "Personally, it was a great outing, a lot of strikeouts."
Getting the call for the Brewers on Friday will be righty Jimmy Nelson, who has lost three of his last four decisions. Nelson lost to the Dodgers on Sunday, as he allowed two runs and eight hits in six innings, dropping him to 2-3 on the year to go along with a 4.00 ERA.
"It's definitely mechanical. It's that, and it's mental," Nelson said. "It's not trying to do too much and just trusting my stuff, trying to get ground balls."
Milwaukee took two of three from the Dodgers last weekend.