The deceased were identified as Chedi Lal, 70, and his wife Laxmi, 62. Vinay, who was staying with the couple as a tenant, also got injured while trying to rescue them, they said.
Police said that it was suspected that the couple's son, who is mentally ill, allegedly set them on fire and fled.
The injured neighbour told the police that he saw the couple's son fleeing from the spot.
Police said that the fire broke out at 3.25am on the ground floor of the building in which the couple was injured. They were admitted to a hospital where they were declared brought dead, police said.
Locals claimed that the couple's son used to physically abuse his parents.
Another neighbour claimed that he used to forcibly take away money from his mother and would often create ruckus in and around the house.
The couple was staying in a 2BHK house and Lal ran a chaat shop. Their other children also expressed suspicion about their brother's involvement in the incident and said that he would beat his parents and torture them, police said.