A blaze started by a careless smoker in a Harlem apartment left a family of four — including two children — fighting for their lives yesterday, fire officials said.

Firefighters arrived at the 1:50 a.m. blaze to find a family trapped inside a fourth-floor apartment at 271 W. 126th St.

A girl, 5, a boy, 3, a woman tentatively identified as Norma Stubbs, 43, and a man in his 60s suffered smoke inhalation and burns. “They’re all in very critical condition,” said Mulhall.

The girl was transported to the burn unit at New York Hospital, and the boy and two adults were rushed to Jacobi Hospital.