It was the first of two weekend attacks on women in different parts of the city.
Const. Brian Montague said that in the first case, the woman believed she'd hailed a taxi for a ride home from the city's Gastown district at about 2:30 a.m. on Saturday.
He said the woman was driven to east Vancouver, where she was physically and sexually assaulted in a dark-coloured minivan with sliding doors on both sides.
Montague said the victim managed to break free and run to a passerby for help.
"She is extremely traumatized as well as physically injured," he said.
Montague said the suspect has been described as a 35- to 39-year-old overweight aboriginal man with big belly and a shaved head.
Police are appealing for the public's help in finding the man who may own or have access to the minivan that was mistaken for a taxi.
On Sunday, a 20-year-old student at the University of B.C. was assaulted as she returned to her apartment at about 3:30 a.m.
Sgt. Drew Grainger of the RCMP detachment at UBC said in a statement that the woman was approached from behind by a man who emerged suddenly from a stairwell in the building where she lives.