A hulking 14-year-old boy was busted Monday for raping a woman at gunpoint as she delivered a package on Staten Island, cops and law-enforcement sources said.

The teen — described by law enforcement as a “total stranger” to the 37-year-old victim — was arrested around 10:30 a.m. and charged with rape and a slew of other raps in the heinous Sept. 9 sex attack in Dongan Hills, police said.

The boy, who is about 6 feet tall and 200 pounds, approached the woman as she made the delivery at Dongan Hills Avenue and Jefferson Street around 6 p.m., according to authorities and sources.

He then hit her with a gun and proceeded to rape her, police said.

The victim was taken to a local hospital, where she was listed in stable condition.

But the teen fiend, shown in an NYPD sketch with a mask covering half his face and a hoodie pulled up over his head, had already fled the scene, police said.