The incident took place at around 2 AM when the overloaded bus coming from Haridwar was on its way to Kamalpura village in Sambal district, police said.
While 13 persons were killed on the spot, two others succumbed to injuries in a hospital.
All the victims belong to an extended family and were returning from Haridwar after attending a 'mundan' ceremony.
Shakeel Ahmed, ASP, J P Nagar said, "Investigation and rescue work are on".
The driver fled from the accident spot.
The injured are admitted in Amroha and Moradabad government hospitals.