The captain and his co-pilot on Airbus A330 were suffering from fatigue and had decided to take turns with 20-minute naps during long-haul flight into the UK on August 13.
But both nodded off at the same time soon after take-off with the plane left cruising on autopilot with no-one to take control in the event of an emergency, according to a Freedom of Information request by the 'Data News' agency.
The UK's Civil Aviation Authority (CAA) did not identify the airline or where the incident occurred.
"This was a serious incident but an isolated one. I think lessons will be learnt from this. We are circulating this report within the industry," a CAA spokesperson said.
"We don't know why the pilots had so little sleep before this flight. They were taking it in turn to have rest periods, with the one always checking the autopilot and it looks as if both fell asleep at the same time," the spokesperson said.
One of the pilots reported that they had only five hours' sleep over the previous two nights.
The British Airline Pilots Association (BALPA) has warned that long shifts leading to fatigue is a major problem and proposed changes to flying rules being voted on in the European Parliament next month would lead to pilots working up to seven starts in a row and being awake for as many as 22 hours.
"British pilots want to make every flight a safe flight and tiredness is the biggest challenge they face. The CAA has been far too complacent about the levels of tiredness among British pilots and failing to acknowledge the scale of the underreported problem," Jim McAuslan, BALPA general secretary, said.