A crazed driver looking for sex yesterday struck and killed a beloved Brooklyn grandmother after he tried to get her daughter into his car because he thought she was a hooker, police said.

The women had flagged down the four-door burgundy sedan, believing it was a livery car cruising for riders, they said.

Investigators said the drama unfolded about 4 a.m. as Eunice Washington, 54, and daughter, Santana, 29, waited for a bus at Linden Blvd. and Eldert Lane.

Washington and her daughter were returning home after a visit with the infant daughter of her son Ivan - her first grandchild.

Investigators said Santana hailed the sedan to save an hour's wait for a bus.

When Santana tried to get into the backseat, the driver told her to come up front and said he'd pay her when they got to his house, a police source said. The suggestion that she was a prostitute enraged Santana, who with her mother and brother began shouting at the rattled would-be "john", the source said.

Without warning, the driver, described only as a dark-skinned man, drove up on the sidewalk in reverse and slammed into Washington, then sped away. Washington was dead on arrival at Brookdale University Hospital.

Washington's friends and neighbors at the Crown Heights Houses on St. Mark's Ave., where she lived for the last 21 years, were stunned by her death.

"She was a great person," said Dallas Gainey, 23, of the woman everyone knew simply as "Miss Eunice."

Police are asking anyone with information to call (800) 577-TIPS.