Wilder was given the nod 115-111 on one card, Fury 114-110 on another and the third scored the fight 113-113.
Both fightrers thought they should have got the verdict.
Fury said: “We’re on away soil, I got knocked down twice but I still believe I won the fight and I believe every man in here thought I won that fight tonight.
“But I’m showing total professionalism here, I’m a true champion and a true warrior. I went to Germany to fight Klitschko, I’ve come to America to fight Deontay Wilder. Bless Deontay Wilder, he’s a top fighting man.
“I was never going to be knocked out tonight. I got put down with some good shots, I showed good heart to get up. I came here tonight and I fought my heart out.”
Fury believes he and Wilder are the two best fighters in the blue riband division, pointedly sending a message to British rival - and IBF, WBA and WBO beltholder - Anthony Joshua.
Fury added: “We’ll do the rematch but we’re going to go away, recalculate, see what’s going to happen. We are two great champions. Never mind an anybody, me and this man here are the two greatest heavyweights on the planet.
“I stepped up after the amount of time I had out the ring, there’s another certain heavyweight out there. (He’s a) chicken - Joshua, where are you AJ?”
Wilder thought he had done enough to see his hand raised, saying in the ring afterwards: “I think with the two knockdowns I definitely won the fight.
“We poured our hearts out tonight, we’re both warriors, we both went head-to-head but with those two drops I feel I won the fight. I didn’t think he had control of the fight, I think I let out just as much as he did, I wasn’t hurt.”
Wilder felt he was too eager to grab the knockout, adding: “I was rushing my punches, that’s something I usually don’t do. Tonight I couldn’t let it go tonight, I was forcing my punches instead of just staying patient and just waiting on it.
“All the build-up for the fight, I wanted to really get him out of there and give the fans what they wanted to see.
“It was just a simple fact that I was rushing my punches. When I rush my punches like that they never land and I’m never accurate. The rematch, I guarantee, I’m going to get him.” Fury started confidently as he looked to dethrone fellow unbeaten fighter Wilder.
Fury, just over three years removed from his famous victory over Wladimir Klitschko in Germany, was 44lbs heavier than his opponent who had only gone the distance once in his 40-fight professional career.
The Briton backtracked after a fierce left hook from Wilder, who seemed slightly unsteady when his foe landed an overhand right in the closing seconds of the opener.
Wilder was unable to close the range as the fight moved into the second as Fury mixed in confident jabs with occasional mind games, putting his hands behind his back or in the air.
A one-two from Fury seemed to mark up Wilder’s left eye in the third and his superior work-rate gave him the edge over the next couple of rounds.
Wilder’s much vaunted power was keeping Fury honest, though, and he was closing the distance as the fight moved into the second half.
Fury landed two crunching right hands and used his trademark awkward movement to prove elusive in the seventh as Wilder went swinging wildly.
The 30-year-old seemed to be showing no sign of ring rust in his first significant bout since that night in Dusseldorf.
But Wilder finally found his range and a booming left hook and a glancing right put Fury down in the ninth.
The Briton got up at the count of nine and survived the round as Wilder went in for the kill.
Fury shrugged off the knockdown in the 10th and was routinely first to the punch against a Wilder who seemed to be slowing, perhaps fatigued by his efforts in the previous round.
Wilder’s body shot appeared to give Fury pause for thought in the penultimate round but the American probably needing a knockout heading into the final three minutes.
He got a stunning knockdown as Wilder’s vaunted right landed in the opening minute of the 12th.
Fury looked to be out for the count but somehow rose from the canvas and then, staggeringly, pushed Wilder back for the rest of the round.
Fury celebrated on the ropes but he was denied on the judges’ scorecards, the knockdown in the 12th, therefore, proving decisive as Wilder retained his world title.