Officers Tiffany Phillips and Carlos Guadalupe, both 12-year veterans, assisted after they were flagged down by a man who was driving near 41st Street and 10th Avenue.
Cellphone video captured the officers in action, and Phillips delivered the baby boy inside the car.
"They are very grateful for us being there at that spot, at that time," Phillips told ABC New York station WABC-TV.
Phillips and Guadalupe had just started their day when a man jumped out of the car and said his wife was going into labor. The couple's 18-month old daughter also was in the backseat.
"He was very frantic and scared," Phillips said.
The couple, who live in Jersey City, had been rushing to Lenox Hill Hospital. Phillips called for an ambulance and leaned into the car, but by then the baby was crowning.
Guadalupe ran into a hotel to get towels. When he came back Phillips was holding the little boy, who wasn't breathing.
"I began to pat his back and to massage him," she said. "Once I did that I heard him begin to cry. His eyes were blinking and he was breathing. That was a great sound!"
The mother and newborn were taken to Bellevue Hospital and were said to be doing fine.
"I got to thank my partner -- A-plus-plus," Guadalupe said. "She held it down and she did her job. She held her composure. She was fantastic."