After injuring the woman and her friend, the accused also shot himself, police said.
The incident took place around 9.45 PM and all the three were rushed to AIIMS, they said.
Kajal and Jatin Sarkar, who work together at a call centre in Noida, were talking outside a park when the accused walked up to them and allegedly got into an argument with them and later fired at them, police said.
The accused is the son of a CISF constable and had used his father's licensed pistol to shoot the two.
Police said that Jatin had gone to meet the woman along with his friend Alok who managed to escape and informed police.
A case has been registered and further investigation is underway.
Jatin and Kajal have sustained bullet injuries on their abdomen and chest respectively, while the accused fired at his forehead.
The accused had been stalking the woman for some time now and suspected her of being in a relationship with Jatin.