Anjali Devi, married with two children, was in an extra-marital affair with the accused, Naveen Uppal (30), for around the past seven years, police said.
Earlier this month, Uppal got married to another woman and wanted to get rid of Anjali, for which he had called her to the Vishwavidyalaya metro station here yesterday for settling the matter. Anjali sat in Uppal's car and both drove towards Bonta park in the campus area, they said.
Uppal then called up Anjali's sister and told her that Anjali had shot herself dead and he was going to commit suicide too. He kept sitting inside the car till the time Anjali's relatives called up the police and a police team found his car near the park.
In the initial stages of the probe, Uppal maintained that Anjali had killed herself with the gun before he could stop her.
Uppal has been arrested under charge of murder and illegal possession of firearms, a senior official said.
Anjali's body with a bullet injury on the head was found yesterday in the car. She used to live in outer Delhi's Rohini with her husband and two children, police said.