New England (7-3-6, 27 points) saw its winless skid reach five games (0-2-3) but showed significant defensive improvement after allowing nine total goals over the previous three games.
Petrovic stopped Gabriel Pereira three times and Santiago Rodriguez twice. He prevented New England from conceding the winning goal late in stoppage time by snagging Rodriguez's right footed shot from the center of the box.
After Petrovic's final save, New England almost scored toward the end of the seven-minute stoppage time, but Emmanuel Boateng's left-footed try from the left side was blocked. Boateng's near miss occurred after Dave Romney and Matt Polster missed the net in a one-minute span shortly before stoppage time.
Luis Barraza made two saves as he returned to goal after Matt Freese made his debut in Wednesday's 3-1 loss to FC Cincinnati. But NYCFC (4-7-5, 17 points) saw its winless skid reach seven games (0-5-2). It was Barraza's second shutout of the season.
NYCFC attempted nine shots in a competitive opening half but only two were on target. In the 18th minute, Petrovic denied Pereira's left-footed try from outside the box and then made a leaping save on Pereira in the 23rd minute.
Petrovic's second save on Pereira occurred moments after New England scored but Bobby Wood's goal was disallowed after he was ruled offsides.
NYCFC nearly scored in the 34th minute but Richard Ledezma's right-footed try from outside the box clanged off the right post.