Greinke makes just his fourth start Tuesday night and first at Miller Park since being traded from the Milwaukee Brewers last season.
The Dodgers have made large investments over the last year, adding high-priced players Hanley Ramirez, Adrian Gonzalez and Carl Crawford through trades before signing Greinke to a six-year, $147 million in the offseason.
Los Angeles (18-25), though, is in last place in the NL West, and Mattingly has taken the brunt of the blame. He addressed rumors of his impending firing before Monday's series opener, saying he'll continue to do his job unless told otherwise by team president Stan Kasten and general manager Ned Colletti.
''As far as any kind of rumors or whatever they are, I talked to Stan the other day. He didn't fire me that day,'' Mattingly said. ''I'm still here. Ned didn't tell me I wasn't going to be here tomorrow or today. That's the way I look at it.''
''It feels good but we still need to score more runs,'' Ethier said after Los Angeles scored fewer than four runs for the sixth time in seven games.
Injuries have contributed to the team's disappointing start as well. Ramirez has played only four games due to a hamstring injury, and Greinke missed more than a month after breaking his collarbone in a fight with San Diego's Carlos Quentin on April 11.
Greinke (2-0, 1.62 ERA) made his first start since that incident Wednesday, allowing one run in 5 1-3 innings of a 3-1 win over Washington.
"The collarbone feels pretty good," Greinke told the team's official website. "It's not 100 percent, but it doesn't restrict me at all when I'm pitching."
Greinke threw only 83 pitches in his last outing, though.
"My stamina needs to grow a little bit, but that could be next start," Greinke said. "It needs to be a little bit stronger throughout the game. I was feeling pretty drained after five."
The right-hander went 25-9 with a 3.67 ERA with Milwaukee from 2011 through July 28, 2012, when he was traded to the Los Angeles Angels. Greinke has never started against his former team, though Yuniesky Betancourt (0 for 10) and Aramis Ramirez (0 for 9, 4 Ks) are hitless against him.
Ryan Braun went 2 for 4 and Betancourt singled for the team's only hits Monday as Milwaukee dropped to 3-15 in May. NL batting leader Jean Segura, acquired from the Angels in the Greinke trade, went 0 for 4 to drop his average to .355 after going 8 for 16 over his previous four.
He has gone hitless in back-to-back games just once this season.
The Brewers (17-26) have lost seven of eight at home and will look to get back on track with help from Hiram Burgos.
Burgos (1-2, 6.58) began his rookie season 1-0 with a 3.00 ERA over his first three starts, but he gave up 12 runs in just three innings of a 13-7 loss to Cincinnati on May 11 before allowing three runs in five innings of Thursday's 7-1 loss to Pittsburgh.
The right-hander faced the Dodgers on April 26, allowing three runs and four hits - including a solo homer to Carl Crawford - in six innings before leaving without a decision in Milwaukee's 7-5 loss.