Greinke (14-3) lowered his major league-best ERA to 1.61 and allowed four hits over seven innings while leading Los Angeles to its first sweep of a series in Cincinnati since a three-game set in July 2009. He finished with two walks and nine strikeouts.
He improved to 7-2 in 12 games against Cincinnati.
Chris Hatcher pitched the eighth and allowed Todd Frazier's fly ball to left field that Andre Ethier caught one step in front of the wall. Jim Johnson pitched the ninth for his 10th save.
The sweep helped the West Division-leading Dodgers salvage an eight-game road trip that started with five straight losses, including a no-hitter by Houston's Mike Fiers last week.
The Reds finished 1-9 on their homestand and have lost 12 of their past 13 games.
The Reds didn't get a runner to third base until the fifth inning, but Jay Bruce was stranded when pitcher Anthony DeSclafani bunted foul with two strikes and Skip Schumaker struck out.
Justin Turner, Andre Ethier and Yasiel Puig led off the second with consecutive singles against DeSclafani, setting up Yasmani Grandal's bases-loaded run-scoring double-play ball.
The double play was the first of five turned by the Reds in the game.
DeSclafani (7-10) allowed six hits — three by Ethier — and one run with one walk and six strikeouts in seven innings while losing his third consecutive start.
Relief pitcher Juan Nicasio was called in from the bullpen to pinch-run in the ninth when Yasiel Puig appeared to pull a leg muscle while beating out an infield hit.
Dodgers: 1B Adrian Gonzalez left Thursday's game after four innings with a right knee contusion. Gonzalez fouled a ball off the knee in the third inning. He's day to day. Gonzalez grounded out and struck out in his two at-bats.
Reds: LHP Sean Marshall remains on his throwing on every third day program as he works his way back from May shoulder surgery. He resumed throwing off bullpen mounds on Aug. 5. "At some point in time, we'd like to see him face live hitters, but we need to see a little more arm strength and a little more familiarity with the breaking ball," manager Bryan Price said on Thursday.
Dodgers: Clayton Kershaw (10-6, 2.29 ERA) is scheduled to start Friday's opener of a three-game series against the Cubs at Dodger Stadium. Kershaw is 5-0 with a 0.90 ERA over his past nine starts.
Reds: RHP Raisel Iglesias (3-5, 3.93), who's coming off a 13-strikeout performance in a 4-0 loss to Kansas City last Sunday, is scheduled to start Friday's opener of a three-game series at Milwaukee.