With barely a lap to go, Sifan Hassan pushed his way to the front and attempted a patented long sprint.
She was part of the reasoning but couldn't take the race and finished sixth.
Tsegay had a tough showdown with Kenyan Beatrice Chebet who finished second.
World record holder Letesenbet Gidey, who won the 10,000 earlier in the championship, lost rhythm after Hassan's push and finished no better than fifth but was delighted with Tsegay's victory.
With the victory, Tsegay took his first major title.
In connection with the finish, three celebrating men entered the arena and rioted, one of them lifted Tsegay and Gidey around, before they were ejected by police.