The woman is hospitalised and critical while Amit (25) and his cousin Basant (19) have been arrested, said a senior police officer.
The incident happened around 2 PM yesterday at the woman's house and her three-year-old niece was witness to the gruesome attack, police said.
The victim's condition is said to be critical and isn't in a condition to record her statement, they added.
The incident took place in Dharampura colony when the victim, who works as a teacher at a play school, was at her home along with her three-year-old niece, police said.
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The niece somehow managed to alert the neighbours but the accused had fled by that time, they said.
The accused had bought two knives and stabbed her nine times on front and back, police said.
The accused had been talking to her brother for last four months and wanted to woo her, they added.
Three months back, he had got married and the victim told him that she didn't want to stay in touch with him, police said.
"He meticulously planned the murder and purchased two knives to execute it. The weapon of offence has been recovered. To make sure the girl was alone at the time of the incident, Amit had even called her brother outside on the pretext of some work," said a senior police officer.
He involved his cousin Basant as he was close to him and he had even agreed to execute the plan.
The girl is being treated at Safdarjung hospital and her condition is said to be critical.
A case under section 307 (attempt to murder) has been registered. Further investigation is underway. Both the accused are unemployed.