However, the judges still returned mixed scorecards with Alejandro Rochin marking Wilder as a wide victor at 115-111, Robert Tapper favouring Fury at 114-112 and Phil Edwards scoring a 113-113 draw.
Wilder first won the WBC heavyweight title by beating Bermane Stiverne in January 2015, in the only fight to date he'd won not inside the distance, and had defended the title seven times ahead of the Fury fight. I was too hesitant.
Fury's extraordinary Lazarus act however ensured the fight would go to the judges.
He becomes only the second to achieve that feat, but it could have been different.
The 30-year-old Briton, who had boxed skillfully to frustrate and outpoint the aggressive but inaccurate Wilder, looked to have finally been beaten when the American champion uncorked a savage right-left combination that sent him sprawling to the floor.
Surely thinking his eighth successful defence of his WBC strap was secure, Wilder began to celebrate in the ring.
Paris, meanwhile, admitted what she did when Fury got knocked down in the final round.
Take a look at this. "There were about eight thousand travelers and Brits who have come from around the world, 10 thousand", Fury said.
"Only God knows how he got back up...it'll be easier for me to hit him [in a rematch]."
"The world knows who the real WBC champion is". Fury counter-punched his way through the fifth round, though most of the shots he threw upstairs were blocked by Wilder.
Tyson Fury was knocked down twice but had the better of the rest of the fight
It was another boxing scorecard that stunned the world, but when the judges' verdict was read out to a raucous Staples Centre in Los Angeles, Tyson Fury was unusually calm. "Me and this man are the two best heavyweights on the planet".
'There are a lot of homeless people on the streets here, more than I've ever seen ever in my life.
"At the end of the day that [a rematch] is down to Tyson, but from my perspective I'd love the rematch", Warren said.
Fury's struggles with drugs, alcohol and mental health are well known.
The punch wasn't the biggest of the fight, but Fury was stunned - and he responded by getting up and raising his aggression in an exciting round.
Fury also said he hopes to arrange a rematch. "Me and this man are the two best heavyweights on the planet", added Fury, who exited his press conference after leading a rousing chorus of Don McLean's classic "American Pie".
He said: "It's an iconic comeback, isn't it?" But Fury went down again - and almost everybody thought it was for good.
And so a remarkable moment in heavyweight boxing played out.
On the undercard, Jarrett Hurd defended his WBA and IBF 154-pound belts with a fourth-round stoppage of Jason Welborn.
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