The fire broke out at 50 East 191st Street in the Fordham Manor section.
It began in the kitchen of a 6th floor apartment, home to a family of five.
When the fire started, the 28-year old father quickly responded.
"He woke up and seen there was fire," said Chris Camacho, a neighbor.
"So he gave his wife the newborn and told her to run outside, and he went back in the house to get the other two girls."
The 22-year old mother fled the flames of her sixth floor apartment, clutching her three-month old baby boy.
"She was screaming 'My babies, my babies," said another neighbor, Nick Suarez.
"And when I opened the door, everything was filled with smoke and the fire was coming out. And I just saw her there screaming and she was crying hysterically for her kids."
When firefighters reached the two bedroom apartment, the man who had sent his wife and newborn to safety was lying on the hallway floor, unconscious and badly burned.
"I heard some moans, I don't know if he was semi-conscious maybe," firefighter Chris O'Brien said. "He was laying on his side and we were able to pull him out."
Firefighters went back in and rescued the couple's two little girls, ages 1 and 3.
At 3:15 a.m., 9-1-1 operators were bombarded with calls from neighbors, after smoke filled the hallways and the extreme heat made the bricks on the building pop like popcorn.
"We heard popping. That turned out to be the bricks almost exploding because the fire was coming out, it was so hot," said FDNY Captain William Kearns.
Firefighters believe the fire started in the kitchen.
But exactly how it started is still under investigation.
The parents and their three young children were all taken to Jacobi Hospital, all suffering smoke inhalation.
The father is in critical condition, and the children are listed in critical but stable condition.
The mother was treated for minor injuries.
Get Eyewitness News Delivered