Wilder almost knocked Fury out in the 12th round with a hard knockdown, but Fury survived and stormed back for a memorable round of the year candidate in a fight that likely will see a sequel.
Wilder thought he had done enough to win the fight.
The three judges were divided on the outcome, with one scoring it 115-111 for Wilder, another 114-112 for Fury and the third 113-113.
American Wilder recorded two knockdowns as he retained his WBC title at the Staples Center in Los Angeles, as well as remaining unbeaten in his professional career.
While both men thought they won, neither was overly upset by the verdict in front of a frenzied Hollywood crowd.
Fury ducked and weaved
With just two minutes left in the fight, a vicious right-left combination from Wilder left Fury flat on his back.
Lewis believes the majority draw result showed "how hard it is for a Brit to come to America and take someone's belt" when Fury overcame two knockdowns in the Staples Center in Los Angeles on Saturday night, including one particularly devastating hammer blow which left him prone on the canvas in the final round.
"I'm not going to sit here and complain, and scream robbery or whatever", Fury said.
Manny Pacquiao, who has won world titles in eight weight classes, added on the social networking site: "Respect to Fury for sticking to his game plan and to Wilder for closing the gap with two huge knockdowns!" Although he didn't land it with full force, he dropped Fury, who did not seem badly hurt.
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"The rematch, I guarantee I'm going to get him", Wilder said.
Wilder, the more aggressive of the two fighters early on, quickly moved into an early lead.
"I would love for it to be my next fight", Wilder said of the rematch. "It was a great fight and let's do it again".
"We gave more attention to the defensive phase today in order to kill the match and got a very good reaction for the level of application and attention. The world knows I won the fight", Fury said.
Late in the round, Fury threw his hands in the air and wagged his tongue, imploring Wilder to come at him.
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But early in the ninth, Fury went down when he absorbed a shot to the top of the head from Wilder.
"In a rematch, I can only imagine that he will be even better prepared".
"We can only do our best in that ring, no matter what anyone says, Deontay is a great champion", Fury said.
In ballyhooed a matchup of two towering men for the WBC heavyweight title, Tyson Fury and Deontay Wilder displayed everything but settled nothing. "That's what we proved tonight, and I'm ready to do it again".
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