A crew of dapper robbers in suits and fedoras busted open a Tourneau display case in Midtown on Tuesday and ran off with dozens of pricey watches Tuesday, police sources said.

The three bandits walked into the Madison Avenue shop near 53rd Street at around 1:20 p.m. — and made a beeline for a Rolex case in the back of the store, according to the sources.

Two of them smashed open the case with hammers and the other fired two shots from a semi-automatic handgun into the floor and toward a retail worker, the sources said.

Within seconds, they stuffed several dozen Rolexes into duffel bags and bolted out the front door, police sources said.

“Everybody was freaking out and screaming — then they fled,” a police source told The Post.

A retired police officer who works at the store heard the commotion and chased the crooks up Park Avenue, police sources said. He collared one of the men — a 19-year-old — and flagged down a police officer, who busted him with “a few” watches, according to police.

The other two men ran into a subway station and got away.

Shoppers were stunned by the sound of gunfire.

“People were running away from the store and covering their heads like they heard gunshots,” said a nearby ice-cream vendor, who asked not to be identified.

“I was worried, so I left my station and walked into the store to check on everyone to see if they were OK,” he added. “I saw all the employees were hiding under their desks in the back of the store. It was horrible.”

The bandits had “satchels strapped across their sides,” he added. One of them wore a bow tie, according to police sources.

A worker at the watch shop was scratched with glass during the stick-up, cops said.

Cops credited the retired cop for thinking quickly.

“There was a retired police officer inside the establishment. He did not fire any rounds. He did pursue the men afterwards,” Chief of Manhattan Detectives Bill Aubry said at a press conference Tuesday.

A store representative couldn’t be immediately reached for comment.

Police did not identify the ­19-year-old suspect or the retired police officer.

Additional reporting by Frank Rosario and Natalie O’Neill