The 25-year-old -- who two years ago denied British legend Mo Farah gold in his last track final -- came home in a time of 12 minutes 58.85 seconds.
His compatriot Selemon Barega, 19, took silver in 12:59.70 and Canada's Mohammed Ahmed the bronze in a time of 13:01.11.
There was no joy for the three Norwegian Ingebrigtsen brothers.
European champion Jakob fared the best, after Henrik was dropped early on and Filip having been prominent faded with over two laps to go.
Jakob, the youngest of the three, set sail for home 350 metres out and opened up a sizeable gap on the pursuing Ethiopians.
However, the 19-year-old had no answer as Edris and Barega came after him round the curve of the final bend.
Jakob, who will also contest the other event he is European champion in the 1500m along with his brother Filip, was a spent force and Ahmed caught him.
Ingebrigtsen collapsed on crossing the line lying head down on the track.