Sporadic thick right hands from Fury had Seferi on the back-foot in the fourth, and his corner evidently made a decision to spare him further drawn-out punishment when they summoned Edwards and withdrew their man at the end of the round.
The Gypsy King defeated Sefer Seferi on his long-awaited return to the ring at Manchester Arena on Saturday night.
Following his victory, the British boxer described the return to the ring as "fantastic".
He never looked troubled against Albanian opponent Seferi, ten years his senior and nearly a foot smaller than the Briton, in what proved to be a farcical match-up.
"He took me a few rounds so I'm happy with it".
"We keep moving onward and keep moving forwards and the objective is to get him into contention to fight for the world title as soon as possible".
From the moment Fury lifted Seferi off his feet during the pre-fight weigh-in, it was clear his comeback was unlikely to go down in the heavyweight annals, and Seferi duly obliged.More news: Trump and Kim Jong Un will begin summit with one-on-one meeting
"I could have knocked him out in the first round but what good would that have done me?" I got four rounds instead of ten seconds.
"He took a couple of hard punches and he told his corner not to send him out for round five. I am determined to enjoy my career this time around and not take anything for granted".
Seferi is 39, has not boxed at an elite level, was 7 inches smaller and almost 70 pounds lighter than Fury.
It was always comfortable for Fury in his first fight since winning the World Boxing Association (WBA), International Boxing Federation (IBF) and World Boxing Organisation (WBO) titles from Ukraine's Wladimir Klitschko on points in November 2015.
Fury was eventually given a backdated two-year ban and in his exile he piled on the pounds.
His promoter Frank Warren is evidently intent on keeping Fury busy as he begins his long road back towards the top, and he is next scheduled to fight at Windsor Park in Belfast on August 18.
Warren plans to keep Fury busy but has no idea yet who he will face in his next fight at Windsor Park in Belfast, Northern Ireland, on August 18.