Sloppy defense hurt the Marlins for the second consecutive night. They committed a season-high three errors, including two in the Dodgers' three-run fourth inning.
Two Marlins errors led to two unearned runs in their 6-4 loss Tuesday.
"We've got to pick it up defensively. We're making way too many mistakes," manager Mike Redmond said. "We can't make a lot of mistakes, especially against such a good team."
Greinke allowed one run in eight innings and won his fourth start in a row. The right-hander improved to 12-3 and tied major-league ERA leader
Clayton Kershaw and
Hyun-Jin Ryu for the team lead in victories.
Greinke said there's no rivalry among the Dodgers pitchers, not even a friendly one.
"Kersh is on such another level that if you try to do better than him, you're going to get your feelings hurt," Greinke said.
Actually, Greinke has been tough to top lately, with an ERA of 0.41 over his past three starts.
Greinke allowed Miami six hits, walked none and lowered his ERA to 2.91.
Yasiel Puig was back in the Dodgers' starting lineup. He appeared to tweak his lower left leg in the early going and limped slightly at times but stayed in the game.
Puig went 0 for 5 and is batting .167 (7 for 42) over his past 11 games. The rookie sensation was back in right field after being held out of the starting lineup for one game because of his slump.
"He has some good swings, I thought," Dodgers manager Don Mattingly said.
The announced crowd of 24,996 included Puig's friend, James. The Miami Heat star sat next to one of the aquariums along the backstop and drew the night's biggest cheer when he was shown on the video scoreboard as Puig stepped to the plate.
"I think Puig thought it was for him," Redmond said. "That was kind of funny."
Ex-Dodger Nathan Eovaldi (2-4) hit 100 mph on the radar gun and allowed only two earned runs in seven innings.
"Eovaldi is going to be a monster," Redmond said. "This kid has so much upside. He's still a work in progress. He's going to be a dominating pitcher in this league for many years to come."
But Eovaldi was again hurt by the poor run support that has plagued him this season, and fell to 0-4 in his past seven starts.
"I felt good," the right-hander said. "Fastball command was there, off-speed stuff was there. I just had that bump in the road in the fourth inning."
Puig reached on a wild throw by third baseman Ed Lucas to start the fourth, and Los Angeles took advantage of the mistake.
Hanley Ramirez doubled home a run,
Andre Ethier put the Dodgers ahead with an RBI single, and Ramirez came home on a wild pickoff throw to first by Eovaldi to make the score 3-1.
Stanton's 16th homer put the Marlins ahead 1-0. Aside from that, only two Marlins reached second base against Greinke, and one was picked off.
Los Angeles had only seven hits and went 2 for 13 with runners in scoring position.
Much of the Dodgers' offense came from Ramirez, who had two hits, scored twice and drove in a run against his former team.
Kenley Jansen completed the six-hitter by pitching the ninth for his 21st save in 24 chances. He gave up a walk before center fielder Ethier made a long run and caught Adeiny Hechavarria's drive at the base of the wall to end the game.
That put Miami (48-77) back on pace to lose 100 games.
The Dodgers improved to 27-5 since the All-Star break, and they've won 21 of their past 24 road games. They're unbeaten in their past 18 series since mid-June.
Notes: Ethier had two hits to improve his career average against Miami to .395. ... Stanton had two hits and is 7 for 13 in the series. ... Greinke improved to 3-0 in five starts against the Marlins.