The attack occurred sometime between 8 p.m. and 10 p.m. Friday at the university's Towers at Centennial Square, police said.
The victim was visiting with her friends and went into the building to go to a party there. She waited in the lobby while her friends tried to find the resident who was hosting the party, according to police.
While the woman was alone, a suspect approached her and said, "I know where you're going. You can come with me," police said.
She followed the suspect into an elevator, and while the doors to the elevator were closing, she saw that her friends had returned and tried to get out, but the suspect grabbed her from behind and held her as the doors closed, according to police.
The victim, still believing that she was going to a party upstairs, was then led to a room on an unknown floor where the suspect sexually assaulted her, police said.
She was eventually able to escape and reunite with her friends, and reported the attack to campus police.
The suspect is described as a mixed-race man between 18 and 22 years old who is about 5 feet 8 inches tall and weighs about 180 pounds.
Anyone with information about the case or the suspect's identity is encouraged to call university police Inspector Abe Leal at (415) 338-7200 or (415) 338-2222.