The incident occurred in the afternoon in southeast Delhi's Okhla area when the woman was at home with her two daughters and the accused, who is her husband's nephew' barged in, they said.
She was killed in front of her two daughters by the man who then tried to kill himself by consuming poison and stabbing himself with the same knife, police said.
He then fled the spot after the woman's daughters raised an alarm, a senior police officer said, adding the she was rushed to hospital but could not be saved.
The accused walked for nearly two kms to reach the nearest metro station, but collapsed near the station. Police soon held the man and rushed him to a hospital where he is currently undergoing treatment, the officer said.
The incident came to light around 1 pm when the police were informed about the incident by a neighbour.
Doctors said she had a fatal stab wound in her abdomen, said the officer. The woman's daughters are in shock after the incident.
During investigation, the police found that the woman was living with her husband and two daughters in a rented room near Okhla for the last five years.
The couple worked in a private thread manufacturing factory. Around three years back, her husband's nephew came to live with the couple.
The woman and her husband's nephew entered into a relationship. She broke up with her paramour after her husband learnt about her affair. The nephew was also asked to leave the house by her husband, police said.
He shifted somewhere else but a around a couple of months back, he came back to stay in the same building where the couple was staying, police said.
This afternoon, while the woman was at home with her two daughters, the accused barged into her house. He got into an argument with her and in a fit of rage, stabbed her in the abdomen, they added.