The fifth inning began with a Marlon Byrd single and a Tucker Barnhart double during a scoreless game, but Greinke escaped with only Billy Hamilton's sacrifice fly driving in the Reds' lone run.
In the seventh, Byrd doubled with one out and Barnhart walked to bring out Dodgers manager Don Mattingly. Greinke remained in the game and got pinch-hitter Skip Schumaker with a sharp lineout to left field and Hamilton's groundout to third base.
"You've got to take advantage of opportunities, and if Greinke's throwing the ball well, you know there's going to be limited opportunities," Reds manager Bryan Price said.
The Reds' five-rookie rotation has had numerous moments this month where it has kept the team in the game but still came up short without run support. On Sunday, it was Anthony DeSclafani, who pitched six innings and gave up only back-to-back homers (including one by Greinke) in the fifth for the difference-maker.
In the last 18 games since the trades of both Johnny Cueto and Mike Leake, the Reds' pitching staff has a 3.48 ERA but the team's record is 6-12. In the just-completed 10-game road trip, the lineup scored 38 runs for an average of 3.8 runs per game.
There have been 10 quality starts produced by the new-look rotation of young guys.
"You want to feel like you're contributing to victories. No one is happy with silver linings -- hey, 'I had a quality start and we lost,'" Price said. "Some of the less-experienced guys are probably just thrilled as anything to be here and have this opportunity and want to make the most of it and want to pitch well, but ... it's certainly a much more empty feeling at the end of the day if you don't win the game."
It's no coincidence what happens when the Reds offense is flowing in the same direction as their pitching. In back-to-back wins on Wednesday and Thursday, the Reds produced a combined 17 runs. On Tuesday, they scored six runs but only after Michael Lorenzen and Dylan Axelrod fell into an 11-0 hole.
"The baseball cliché is that it all evens out and I think it does. I really do. I truly believe that," Barnhart said. "The biggest part of our staff is keeping the lineup in the game, keeping the offense in the game. One swing here or there could change the game. Against a guy like Greinke, and then you've got [closer Kenley] Jansen coming out of the bullpen, that's tough eating on a day like that. I thought we battled really well and played hard."
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, follow him on Twitter @m_sheldon and Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.