Police from the 46th Precinct responded to hundreds of emergencies this year – but their response to one Christmas call saved the holiday for a single mother and her nine children who had lost hope.

It all started on Christmas Eve, when a 9-year-old boy walked into the Bronx station house with a letter for the officers.

“Dear Santa,” began the letter, which was written by the boy’s mother, Georgia Brown. “I am writing this letter on behalf of my children . . .”

What followed could’ve melted the heart of a snowman: details of the death of the kids’ father in May; how the family has bounced around from shelter to shelter; how poverty has left Brown unable to buy her kids clothing for school or blankets for the cold; and a wish, at long last, for a filling meal.

“It was a cry for help,” said precinct commander Donald Powers.

And the officers of the 46 answered the call. A hat was passed around, and bills appeared as if by magic. Then an official call came in, a report of a man with a gun. The cops responded, but it turned out to be a false alarm.

Sgt. Michael Ruane took advantage of the fact that there now were dozens of cops milling around. He showed the letter, and the hat was again passed – $300 was collected in seconds.

“They all dove into their pockets,” said Ruane. “They just saw the letter and said, ‘This has to be done.’ It was all about the kids.”

With the money in hand, Ruane, joined by Officers Walter Morris and John King, and the precinct’s community council president, Louella Hatch, began their errands of mercy.

First stop was a supermarket, to pick up fresh food and canned goods. Next, a trip to a department store for jackets, blankets, diapers, soap and toothpaste. Later, a run to a restaurant for a chicken dinner for 10.

And toys for the kids – even though the letter didn’t ask for them.

And when the Santas of the 46th Precinct finally arrived at Georgia Brown’s door in Grand Concourse, there were smiles all around.

“You had grown men tearing up,” Ruane said of his fellow officers. “I walked out of there with a little sentimental knot. I didn’t want to rub my eyes, but they felt like they had sand in them.”

All of Brown’s nine kids – from Patty Mullins, 19, to Iesha Mullins, 13, to 1-year-old Amaya – knew that their first Christmas without their father, Leroy Mullins, was saved.

“The police officers’ generosity was unbelievable,” Brown said. “I wrote the letter because I was at my wits’ end. I didn’t expect anything.”

And although he thanked the cops for giving him a Transformer action figure, 9-year-old Aaron Mullins still had one Christmas wish that the men in blue simply could not provide.

“I really wish my family could stay in one house and not in a shelter,” he said.