The 9-year-old Harlem girl who tumbled out a sixth-floor window is in critical condition but should pull through, her mom said Tuesday — as it surfaced that the child was home alone and had been warned by her mother to stay away from the air conditioner minutes before the accident, police sources said.

“By the grace of God, she’s alive,” said Iesha Punter, whose daughter. Kianna, is recuperating in Harlem Hospital. “I’m just gonna keep praying.

“She’s pulling through.”

Iesha declined to detail Kianna’s injuries other than to say she is in critical condition, adding, “I’m just worried about my daughter’s health.”

Kianna was home alone at the St. Nicholas Houses on West 129th Street near Frederick Douglass Boulevard when she fell out of the window at around 5:30 p.m. and landed on a second-story roof landing, police said.

According to cops, the window’s air conditioner fell out first, and when the child was looking down from the window, she fell, too.

She told authorities that she did not know how she managed she fall out of the window, sources said.

Neighbors said the girl could be heard screaming, “Help me! Help me!” after the fall.

Emergency responders then rushed the “conscious and alert” girl to Harlem Hospital.

Sources say the mother and father of the victim and her siblings have an open case with the city Administration for Children’s Services involving domestic-violence incidents in front of the children.

“Our top priority is protecting the safety and well-being of all children in New York City,” said an ACS spokeswoman. “We are investigating this case with the NYPD.”