Sam Solise, 69 - who had already rescued his 6-year- old daughter and the girls' mother - was in "extremely critical" condition at the Staten Island University Hospital burn center.
Firefighters found Rianne Jeanty, 2, in a sink where her dad had placed her as he helped the others get out from the ground-floor window of their Springfield Gardens apartment.
"He put her in the sink while passing the other child out the window. Then, unfortunately, he collapsed," a fire official told The Post.
Solise was found lying on the kitchen floor. He suffered third-degree burns over 60 percent of his body and smoke inhalation.
"My father was a hero," said Stan Solise, 38. "He tried to save his kids before himself. Now he's fighting for his life."
Rianne was rushed to Mary Immaculate Hospital, where she died.
Her mother and sister, whose names were withheld, were taken to the same hospital and released.
The fire broke out at 1:18 a.m. in the apartment at 141-05 Springfield Blvd.
Sam was asleep on a couch in the living room, and the two kids and their mom were in the bedroom when the blaze began near the couch, the official said.
He added that a preliminary investigation points to a space heater as the cause.
There was a smoke detector in the apartment but nobody heard it working, he said, because the battery may have been drained.
Building superintendent Ray Charles Evans was shocked.
"Sam is always cool, always smiling. He loved those kids," he said.
"The little girl was always happy. It's unbearable."
