"Hopefully, that's how it stays," Greinke said.
Greinke was originally scheduled to pitch two days earlier against the San Diego Padres, but his turn in the rotation was pushed back to Saturday because of inflammation in his right elbow.
Greinke was unusually upbeat about his performance, considering he served up two home runs that resulted in four runs for the visitors.
"I thought I pitched really well," he said.
He also downplayed Manager Don Mattingly's concerns about how his arm might feel Sunday morning.
"I think I'm fine," Greinke said. "I'm pretty confident I'll be fine tomorrow."
That would come as a significant relief to the Dodgers, who have already moved journeyman Kevin Correia into the rotation to replace a sidelined Hyun-Jin Ryu.
The team would like for Greinke's comeback to be start of a trend. They are expected to get back another key player Sunday for the final game of the three-game series at Dodger Stadium, as shortstop Hanley Ramirez remains on track to be activated from the 15-day disabled list. Ramirez was placed on the DL on Aug. 10 with a strained side muscle.
"If he's good to go, I plan on playing him," Mattingly said.
While Greinke was far from his best Saturday night, he offered reasons for the Dodgers to be encouraged.
"If you didn't know anything, nobody would have even mentioned anything," Mattingly said.
Greinke (13-8) threw 105 pitches over seven innings. Of the four runs he gave up, three were earned. He gave up nine hits, struck out four and walked one.
The win was his first since July 25 and only the second in his last eight starts.
Greinke appeared to have no trouble warming up, as he threw 12 pitches in a scoreless first inning, all of them fastballs and all between 91-94 mph.
He was also able to pitch out of early trouble. With Travis d'Arnaud at second base in the second inning, Greinke forced Matt den Dekker to ground out to end the inning. An inning later, Greinke gave up a one-out double to pitcher Jacob deGrom, but the Dodgers got out of the inning unscathed, as Greinke got Curtis Granderson to fly out to right field and struck out Daniel Murphy.
The Mets took a 3-0 lead in the fourth inning on a three-run home run by Juan Lagares, and Greinke served up another home run in the sixth inning, a solo shot by Lucas Duda. That homer was the fifth given up by Greinke in his last four starts.
But Greinke wasn't particularly upset with himself for the home runs, saying Lagares and Duda hit well-placed pitches.
Greinke pitched his way out of a jam in the seventh inning to preserve a 5-4 lead. With one out and pinch-runner Eric Young Jr. on second base, Greinke struck out Granderson, intentionally walked Murphy to face David Wright, and struck out Wright for the third out.
The Dodgers scored two runs in the bottom of the inning for a three-run cushion, and the bullpen took it from there.
Follow Dylan Hernandez on Twitter @dylanohernandez