The bus was on its way to Kashi in Uttar Pradesh from Andhra Pradesh when the mishap took place on NH-5 in the early hours, police said.
"Our night patrol vehicle noticed the bus lying overturned. The tourists were screaming for help. We rescued the pilgrims with the help of local people and ambulance staff," said Niranjan Dhir, Inspector-in-charge of Kuakhia police station.
The injured were first admitted to a local hospital, he said adding that five seriously injured persons were later shifted to SCB Medical College and Hospital in Cuttack as their condition deteriorated.