Police said the accused were nabbed after the victim gave the random digits of the vehicle's numberplate.
The woman was waiting to hail a bus to return to her PG home and boarded the van which stopped by offering her a drop, City Police N S Megharikh told reporters.
"She was waiting for the BMTC (Bangalore Metropolitan Transport Corporation) bus along with her friend to return to her PG home and boarded the van which stopped by and offered a drop. Her friend, however, insisted not to board the vehicle, but she (the victim) did not heed her appeal," the Police Commissioner said.
Police said for nearly three hours, the two men drove around deserted places of the Madivala area and raped the woman.
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The men allegedly dumped the woman near a temple. The woman called her sister with whom she stays and friends, who rushed to the spot and took her to the St.John's Hospital nearby.
She was admitted to the hospital on Sunday and discharged yesterday, Megharikh said.
The incident has come as a grim reminder of the 2012 gang rape of a paramedical student in Delhi, who later died, triggering a massive outrage across the nation.
In 2005, a 24-year-old employee of a city-based multi-national firm was raped and murdered by the cab driver who was later sentenced for life.