The incident happened on the night of December 18 at Deralakatta on the outskirts of the city.
The couple was in a car when a group of eight men surrounded them.
The gang threatened to kill the students on their refusal to do so and videographed them in the act and tried to extort Rs 25 lakh from them, threatening to put the objectionable video on the internet, police said.
On the students agreeing to give them Rs three lakh, the gang released the girl to bring the money, while holding the boy captive.
The girl approached a lawyer and lodged a complaint at Konaje police station which led to the arrest of the eight men yesterday.
"Three out of the eight men involved are rowdy sheeters. The arrested were produced before a court which remanded them to three days' police custody," police said.