A Yonkers woman was raped by a stranger on a Midtown street after getting lost on the subway and asking a man for directions, cops said.

The 31-year-old woman was heading to her friend’s house at about 1 a.m. Sunday when she got lost and left the subway system on 51st Street near Broadway in Midtown, authorities said.

She then asked several people for directions before the suspect approached her and began leading her by the arm west toward Eighth Avenue, police said.

He then forced her down a flight of stairs into a basement-area of a building on 51st Street near Ninth Avenue and raped her, cops said.

The suspect ran off and was last seen walking north on Broadway near 52nd Street, cops said.

The woman was rushed to a nearby hospital and treated for bruises to her arm, back and right leg.