A home invader killed a 66-year-old professor in the basement of the victim’s Brooklyn residence Monday night, police said.

The intruder attacked Jeremy D. Safran — a professor of psychology at the New School — at about 6 p.m. at 155 Stratford Road in Flatbush, cops said.

The 28-year-old suspect is believed to have followed Safran’s daughter to the location, where he briefly spoke to her in an apparent effort to case the home, sources said.

A neighbor later saw him break in and called the daughter — who at the same time heard sounds of violence coming from downstairs.

Someone then called 911, sources said.

Cops found Safran, who has a Ph.D., on the floor. A hammer lay next to his body and the attacker was hiding in a closet.

The man, whose name was not released, was arrested without incident and was being held at the 70th Precinct.