The three-alarm fire broke out inside a building on West 165th Street in the Highbridge section.
5-year-old Elijah Artis, 2-year-old Jeremiah Artis, and 4-month-old Michael Turner were killed in the fire.
Their 25-year-old mother, 4-year-old sister, and 4-month-old baby sister were taken to Lincoln Hospital where they were being treated for smoke inhalation.
Neighbor Eddie Tate took one of the girls from her mother, and carried her to safety.
Ten other people from surrounding apartments were treated for smoke inhalation, but none had life-threatening injuries.
A spokesman for Con Ed says power had been cut off to the family's apartment for non-payment.
According to neighbors, the mother had gone to the bodega downstairs and bought candles to light the apartment.
Fire marshals said the apartment did not have smoke alarms.
The mother had been approved for public assistance, and the lights were due to come back on Saturday.