The Dodgers were in an unfamiliar position of late, trailing early on Sunday.
In the Dodgers’ six wins over the Mets in the previous nine days, New York had only three singles in 47 at-bats with runners in scoring position.
Price needed 33 pitches to get through the first, but retired 10 of his final 11 batters faced, throwing 42 pitches over the next three scoreless frames.
Cody Bellinger’s two-run single in the fourth inning pulled the Dodgers to within a run, and put runners on the corners with two outs.
But he recovered to get the next two batters, including a nifty play by shortstop Corey Seager for the second out.
The Dodgers intentionally walked catcher Pat Mazeika to load the bases for the pitcher’s spot, and Mets manager Luis Rojas opted to let Marcus Stroman bat, sitting on 81 pitches through five innings.
On Sunday he took a Chris Taylor smash off his throwing hand at third base, and was hit by a 100-mph pitch from Graterol in the sixth.
Shane Greene pitched an imperfect ninth, allowing a single, hitting two batters, walking in a run while recording only one out.
The Dodgers have used 21 different pitchers in relief in August, two more than any other month in franchise history.
Julio Urías is expected to be activated off the injured list to start the opener for Los Angeles.