A clueless crook made off with a Queens couple’s luxury car — and was nabbed when he called 911 to report the stolen ride missing from a Big Apple parking garage, according to federal prosecutors.

Rustambek Zokirov, 24, is accused of stealing the 2019 Mercedes-Benz after a violent home invasion robbery in Flushing, Queens, in which the feds said he identified himself as an FBI agent to target the local couple on July 16.

Zokirov and another fiend allegedly tied up the pair, blindfolded them, held them at gunpoint and Tased them over the course of several nightmarish hours, according to a criminal complaint filed in Brooklyn federal court.

“Zokirov and the accomplice then stole various items, including credit cards, designer handbags, luxury jewelry, a cellular device owned by one of the victims, keys to the victims’ Mercedes-Benz and approximately $30,000 in cryptocurrency,” the complaint alleges.

To make their getaway, the two crooks set up a 15-minute timer, loosened the restraints on the victims and warned them to wait before freeing themselves, according to the court document filed last week by the US Attorney’s Office in Brooklyn. The shaken-up victims called the NYPD at 11 p.m. to report the robbery.

Zokirov allegedly drove off in the Mercedes and got away with the stolen goods — at first.

On July 19, the stolen car was spotted at a Manhattan parking garage and was seized by cops, prosecutors said.

Zokirov returned to pick up the car the next day and asked for the keys — even showing the parking attendant his actual driver’s license — but was told cops had seized the vehicle, according to the court docs.

Rather than high-tail it, Zokirov called the cops himself — and was busted when they showed up, the filings state.

Prosecutors asked a judge to order Zokirov be held without bail pending trial, calling the accused thief “extremely dangerous.”

Zokirov and his alleged accomplice, Cheng Wei Huang, 24, are both charged with robbery and impersonating federal agents.

Zokirov’s lawyer declined to comment when reached by The Post on Monday.