All three of them were rushed to Deen Dayal Upadhyay Hospital, where the toddlers -- one aged two years and the other around 10 months -- were admitted, but the woman was declared dead, said a senior police official.
The incident was reported between 2 PM and 2.30 PM when neighbours heard the children crying uncontrollably.
According to police, when the loud cries stopped after sometime, a neighbour went to check on the family but found the door locked from inside. On peeping through the window, the neighbour saw the woman's body hanging and immediately called up her husband, who is a plumber.
Later, a police team broke open the door and rushed all three of them to the hospital.
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While the two-year-old boy suffered severe injuries on his throat, the 10-month-old boy had an injury on his head.
Both of them were found lying unconscious inside the house, said the senior official.
From preliminary investigations, it appears that the woman allegedly tried to strangle the elder child and the younger one was dropped from a height capable of inflicting deep injury.
When she was convinced that the children were dead, she went to the adjacent room and hanged herself to death from the ceiling fan with a stole, said the official.
The cops are also questioning neighbours for viable leads, said a police official.
The woman and her husband are both natives of Odisha. They got married in 2006 and later moved to Delhi. Their eldest son, who is eight-year-old, lives with his grandparents at their native village in Odisha, the official said.
A case has been registered under relevant sections of IPC, the official said, adding further investigations are on.