The 33-year-old Wilder effectively retained his title in the dramatic final round with the second of two knockdowns, one so heavy Fury appeared out cold before remarkably returning to his feet.
A rematch appeared inevitable even before it was controversially announced a draw via scores of 115-111, 114-112 and 113-113 and owing to his classy, gutsy performance as he outboxed the champion, Fury would surely be the favourite.
Unusually since Anthony Joshua’s victory over Wladimir Klitschko, the IBF, WBA and WBO champion would be at risk of being overlooked as the division’s leading attraction, and discussing the inevitable rematch, Fury said: “One hundred per cent we’ll do it.
“We are two great champions. Me and this man are the two best heavyweights on the planet.
“We’re on away soil, I got knocked down twice, but I still believe I won that fight. I’m being a total professional here. I went to Germany to fight Klitschko and I went to America to fight Deontay Wilder. God bless America. The ‘Gypsy King’ has returned.
“I hope I did you all proud after nearly three years out of the ring. I was never going to be knocked out. I showed good heart to get up. I came here and I fought my heart out.
“I’m what you call a pro athlete that loves to box. I don’t know anyone on the planet that can move like that. That man is a fearsome puncher and I was able to avoid that. The world knows I won the fight.
“I’ve been away from my family for 10 weeks. I’m just going to spend some time with my family. (It’s) well deserved.”
America’s Wilder, who like Fury had previously won each of his professional fights and was the lighter of the two by 42lbs, also argued that he had deserved the decision but he said: “I would love for (a rematch) to be my next fight. Why not?
“Let’s give the fans what they want to see. It was a great fight and let’s do it again. It doesn’t matter to me where we do it.
“With the two knockdowns I definitely won. We poured our hearts out. We’re both warriors, but with those two drops I won the fight. I came out slow. I rushed my punches. I didn’t sit still. I was too hesitant. I started overthrowing the right hand and I just couldn’t adjust.
“I was rushing my punches. That’s something I usually don’t do. I couldn’t let it go. I was forcing my punches too much instead of sitting back being patient and waiting for it. I really wanted to get him out of there, give the fans what they want to see.
“When I rush my punches like that I’m never accurate. The rematch I guarantee I’m going to get him.
“We’re the two best in the world and we proved it. When you get two warriors you get a great fight. I’m ready to do it again.”
Despite two heavy knockdowns, a victory greater than even that over Wladimir Klitschko and after only 14 rounds following over two-and-a-half traumatic years of inactivity was prevented by harsh scores of 115-111, 114-110 and 113-113, despite him impressively outboxing the champion, who retains his title.
Fury was first knocked down in the ninth, and again in the 12th when he appeared out cold, but he returned to his feet and recovered enough to survive to the final bell.
If Wilder’s explosive power already posed a significant threat, the biggest question surrounding Fury’s chances was whether he had truly recovered from that period, in which he admitted to taking cocaine, becoming suicidal and lived to such excess he reached an estimated 27 stone.
The answer to that ultimately became clear when, even as their fight progressed into the dangerous final rounds, he somehow performed with the same sharpness that inspired his memorable victory over Klitschko, even recovering from the second knockdown to end their fight on top.
An affair that was expected to be cagey instead produced 12 thrilling rounds that made a rematch inevitable even before the scores were announced.
They are likely to fight again next spring, when Fury would become the favourite, posing a greater threat to Anthony Joshua’s status as the world’s leading heavyweight.
In front of a 17,698-strong attendance, both fighters entertained from the opening bell when they both threw threatening punches and Wilder landed a hurtful right as they briefly fought toe-to-toe.
Demonstrating his confidence with early periods of showboating, Fury often became the more consistent aggressor and while resisting occasional powerful punches he also made the world’s most dangerous puncher swing and miss.
The champion began to fall short with jabs, and watched Fury comfortably take a left uppercut as he pursued the knockout while his left eye began to swell.
Fury was gradually building a convincing lead into the fight’s second half as he landed with several straight rights, even when Wilder’s occasional successes looked the more hurtful.
The final four were always going to be the most threatening when he tired and his reflexes may have waned, and so it gradually proved when after taking a left-right combination, a right hand to the back of the head knocked him to the canvas.
Fury had twice previously recovered from knockdowns to remain undefeated, and this time the 30-year-old fought back and stuck out his tongue in a sign of his self-belief.
Further success in the 10th round when he landed with both lefts and rights and hurt Wilder, 33, again gave him the momentum when it became increasingly clear the champion was running out of time.
He resiliently then retained his title when, despite his exhaustion, a big right sent Fury tumbling and a further left secured so heavy a knockdown his admirable challenge seemed over.
The Briton instead survived as the tired Wilder struggled to force another attack and the stoppage, meaning an immediate rematch will be next.
It was after the unprecedented high of his victory over Klitschko that Fury fell into the darkest period of his life. This performance showed he has convincingly recovered from that, and he may even again prove the best heavyweight in the world.
Fury’s compatriot and promising fellow heavyweight Joe Joyce had earlier secured his seventh professional victory when he stopped Joe Hanks of America in two minutes and 25 seconds.
There was also a fourth-round defeat for British light-middleweight Jason Welborn, who was stopped by a bodyshot from defending IBF and WBA champion Jarrett Hurd.
Wilder had Fury on the canvas twice, including a spectacular final round knockdown, but was unable to get the knockout victory he had promised to deliver at the Staples Center.
Fury was seemingly done as he lay motionless on the canvas in the 12th after a powerful right from Wilder caught him flush and the American followed it up with a devastating left hook.
But the Englishman somehow got to his feet and beat the count of referee Jack Reiss, and even looked to finish a tiring Wilder himself in the final round, catching him several times.
Fury celebrated wildly at the final bell, while Wilder also gestured that he believed he had won.
In the end it was announced there was a split decision before it was declared a draw. The three judges were divided on the outcome, with one scoring it 115-111 for Wilder, another 114-110 for Fury and the third 113-113.