Queens mom Donna Bingert called police to save her from her rampaging son Zachary in 2010, only to turn around and sue the city when cops were forced to gun down the knife-wielding maniac — whom she had let into her home despite having a protection order against him.

On Tuesday, the city agreed to pay her and Zachary’s dad $250,000 over the lifesaving police action.

The mind-boggling settlement by the de Blasio administration involves a federal “wrongful death” suit filed by the parents of the boozing, bipolar 21-year-old Zachary Bingert.

Donna and Alan Bingert claimed in the suit that their son never posed enough of a threat to the officers to justify the shooting — but the mom clearly feared Zachary herself, having taken out a restraining order against him over at least three previous domestic incidents between the pair.

In one violent outburst only three months earlier, Zachary waved knives at his mother when she wouldn’t give him money, authorities said.

But Donna let Zachary into her Glendale home the night of Dec. 22, 2010, because it was cold outside, she told cops. By 9:30 p.m., she was frantically calling 911 saying Zachary had threatened her with a knife.

Three NYPD officers responded to the scene. They went in to the dark home and ordered Zachary not to move and to drop his weapon. Instead, they said, he lunged at them with the knife, and they shot at him nine times. He was pronounced dead at the scene.

The officers were never cited for any wrongdoing.

The settlement drew outrage from cops.

The administration is “making it so easy for the public to get cash from the city,” said one police source.

“The mayor is willing to give them whatever they ask for or something close to it. It’s starting a bad precedent that you can sue the NYPD, and no matter what, the city will settle,” the source said.

“The perp had a knife, and the cops shot him. There was an imminent threat. We are trained to use our firearms and neutralize the threat. Period.”

“The facts in this case are clear that this individual posed a threat to the extent that his mother obtained an order of protection against him and that the family called police when he threatened his mother again,’’ said PBA President Patrick Lynch.

“Settling cases like this one only serves to encourage others to file lawsuits where the facts don’t support the basis of their claims.”

But it appears that the city didn’t want to take any chances with a jury after the parents filed suit.

Carla Cheung, an assistant corporation counsel for the city Law Department, signed off on the deal. “This case involved a tragic incident, and settling the matter was in the best interest of all parties,” the Law Department said in a statement.

Bingert’s parents, who do not live together, will split $153,597 of the settlement, with their lawyer receiving the remaining $96,403.

Alan Bingert declined comment and calls to Donna Bingert were not returned, with no one answering the door at her home. Their lawyer, Jeffrey Rich, declined comment.