The three were booked in December 2012 in Udhyognagar police station in the city on charges of robbery, gang-rape and murder.
Judge Girish Kumar Agrawal convicted Kapil Anna and Imran Dillhi Wala, both residents of Udhyognagar in Kota, and Tipu Sultan Aabeed of Tonk district, Special Public Prosecutor Kamal Kant Sharma said. The three convicts are between 22 and 25 years old, he said.
The three were also sentenced to life imprisonment.
Police said the three men broke into the house of Shiva Koli at night and looted jewellery, cash and other items. They gang-raped Shiva's wife, who was sleeping with her minor son in the room, the special public prosecutor said.
The three convicts then shot dead the woman and her son and escaped after placing the boy's body in a box, he added.
Udhyognagar police had on December 6, 2012 filed a case and then arrested the three men after investigation. They have been in jail since.
Thirty-five witnesses have been produced before the court, the prosecutor said.