Cops fatally shot a burglar who pointed a revolver “in the face” of a sergeant trying to detain him in Brooklyn on Monday, law enforcement sources said.

The officers were “within arm’s length” of the man as he attempted to flee from the back yard of a home on 78th Street in Gravesend around 6:30 p.m., according to the sources.

One sergeant and one officer fired when the burglar turned his weapon toward them, the sources said.

“It was close quarters,” Chief of Department James O’Neil said at the scene. “The suspect came over the wall. The sergeant was right there. He had to actually push [the gunman’s] arm away.”

The man was struck once in the chest and once in the neck. He was declared dead at Coney Island Hospital.

A nearby gas station attendant said he witnessed the shooting after a break-in on the third floor of a building.

“I was over here working. I heard a shot,” said the attendant. “I saw the cop jump over the green fence from the construction site, coming this way.”

A second suspect, possibly wearing an orange construction helmet, was still on the loose Monday night.