Aarti Borkar, in her late thirties, and her husband Anil were attacked by three assailants armed with sharp-edged weapons in Panchpaoli area, they said.
Aarti, a former sakha pramukh (branch chief) of Central Nagpur unit of Sena, was stabbed several times when she tried to save her husband who appeared to be the prime target of the attackers, police said.
One of the suspected assailants, Akash Gourkhande, was caught by a mob which thrashed him before handing him over to the police.
Police suspect an old enmity with a neighbour may have led to the murderous assault on the Borkars.
In a release, police said they have rounded up three members of one Kesarwani family - Narendra, Surendra, Sonu and another person, Ravi Khante, and booked them on charges of murder, attempt to murder and criminal conspiracy.
The Borkars were reportedly having a long-standing enmity with the Kesarwanis, their neighbours.