For a time, that plane's autopilot played a pivotal role in keeping the fully-booked flight between the two Scandinavian capitals on course, the Aftonbladet newspaper reports.
"I was extremely tired and had to fight to keep my eyes open," the captain wrote in a report reviewed by the Norwegian newspaper VG, citied by Aftonbladet.
However, the sleep deprived-pilot lost the battle to stay awake after his co-pilot left the cockpit to go to the toilet.
When the co-pilot attempted to return, he was forced to buzz the locked cockpit door repeatedly before the pilot woke up and let him in.
In explaining the incident, which took place last year, the captain said he had had less than four hours of sleep. The Copenhagen to Stockholm flight was his fourth of a scheduled five flights he was to pilot that day.
A manager at SAS told VG that, while having a pilot fall asleep midflight is unusual, the airline wasn't planning to take any disciplinary measures against the pilot.