Cops have busted the guy who allegedly sucker-punched and stabbed a black woman in November, leaving her with a collapsed lung, officials said Tuesday.

Aleksejs Saveljevs, 33, was already cooling his heels on Rikers Island for allegedly attacking a cop on Nov. 8 when police charged him Monday with the Nov. 9 hate crime — thanks to a DNA match.

Cops say Saveljevs attacked 57-year-old Ann Marie Washington inside the Church Avenue Q train subway station in Brooklyn. He allegedly came up from behind Washington, called her a “black bitch” and began pummeling her, even stabbing her in the back, according to police sources.

Washington, who was on her way home from work, didn’t realize she had been stabbed until after she had returned home. She was taken to Kings County Hospital and treated for a collapsed lung.

Saveljevs was charged with attempted murder, assault as a hate crime, aggravated harassment and criminal possession of a weapon for the incident.