Wilder (40-0-1, 39 KOs) had tremendous difficulty in finding a rhythm and was largely relegated to throwing single punches, most of which were easily defended by Fury.
"We're on away soil, I was on the ground twice but I truly believe I won that fight, and I think everyone in here did too", Fury said, per the Telegraph.
The judges scored the bout 115-111 to Wilder, 114-112 to Fury and 113-113.
A bout that was supposed to at least put public pressure on Anthony Joshua (22-0, 21 KO), the owner of the WBA, WBO and IBF heavyweight titles and the biggest draw in the division, to face the victor at some point in 2019 - especially if it was Wilder - instead may have tabled that fight for the time being.
While both men felt they had done enough to win the fight, both accepted the result.
With just two minutes left in the fight, a vicious right-left combination from Wilder left Fury flat on his back. Boxing definitely won and Tyson Fury won the fight to me. That's a lesson I learned a long time ago but I went back to it. "I don't know how he got up", the 33-year-old added. But Fury went down again - and almost everybody thought it was for good. Wilder struggled to land a punch as Fury's constant movement kept the champion off balance. From our side we want that undisputed fight ASAP, and that's Deontay Wilder in April 13 at Wembley.
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Whilst the judge who scored so heavily in favour of Wilder has been criticised, the officials have come under fire for not recognising what looked to some observers like a clear foul.
"One hundred percent we'll do the rematch".
Speaking on BBC Radio 5 live's boxing podcast, Costello said: "It has created all this controversy and debate, but it came at the end not of a stinker, as many of us feared, but it's a draw that we are all talking about - it's contentious for me, rather than controversial".
"The rematch I guarantee I'm going to get him". I know when I try to get them out of there the plan goes.
Late in the round, Fury threw his hands in the air and wagged his tongue, imploring Wilder to come at him. Fury managed, somehow, to return to his feet before the count ended.
But early in the ninth, Fury went down when he absorbed a shot to the top of the head from Wilder. "Me and this man are the two best heavyweights on the planet". It doesn't matter to me where we do it. Opinions were divided on the judges' decision, however, with some claiming that Fury was robbed of one of the greatest comebacks in history despite two knockdowns.