A man was viciously beaten to death outside a subway station in downtown Brooklyn Tuesday afternoon — and his attacker was caught hours later by transit cops in Times Square, according to police and sources.

The battered victim was unconscious and unresponsive with severe injuries across his face and body when cops found him outside the Jay Street-MetroTech Station near Lawrence Street and Willoughby Street around 3:07 p.m., police said.

Sources said the assailant — believed to be a man in his 20s — pummeled the victim’s face repeatedly and stomped on his head up to 15 times, leaving him with a fractured skull.

The ruthless suspect then sifted through the victim’s wallet, backpack, and pockets before violently tossing him around, sources told The Post, referencing footage of the heinous attack.

The victim — a man in his 50s who police have not identified — was taken to New York-Presbyterian Hospital Brooklyn Methodist in critical condition and pronounced dead at 4:33 p.m., according to cops and sources.

It’s unclear what prompted the beatdown.

The suspect — last seen wearing black pants with a yellow stripe, a dark shirt with white lettering, and blue loafers and socks — was arrested shortly before 10 p.m. in Times Square, sources said.

The investigation is ongoing.

Shortly after the fatal assault, a 43-year-old man was slashed in the face and the back of the neck with a knife in the mezzanine of the Jackson Heights-Roosevelt Avenue station in Queens at 3:50 p.m., cops said.

The victim was rushed to Elmhurst Hospital in stable condition.

A knife was recovered at the scene, but no arrests have been made.