While Fury (27-0-1, 19 KO), was significantly hurt after both knockdowns, in both rounds he rallied back to actually stun Wilder before those rounds ended.
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.
Eddie Hearn of Matchroom Sports, which promotes Joshua, stayed up to watch the fight from England and told ESPN.com via email: "I had Fury winning the fight as most did". I'm a professional athlete who loves to fight. (When he got up) I was sitting there going "Oh my god". The Alabama native crashed a right hand just above Fury's ear in the eighth, sending him to the canvas. It was a buzzkill ending to what had been an entertaining fight in which Fury used constant movement and sharp punching to win rounds, while Wilder waited patiently to land the big punch.
"At the end of the day that [a rematch] is down to Tyson, but from my perspective I'd love the rematch", he said. "I don't know anyone on the planet that can move like that", Fury said.
Having suffered with depression, alcoholism and drug addiction, Fury's return to boxing and impressive performance in a draw with WBC world champion Wilder has inspired many.
"We're on away soil", he said. "I was never going to be knocked [out] tonight".
Fury's match-up with Wilder is one of the most anticipated fighters in recent times, with both arriving at the Staples Center in Los Angeles undefeated.
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Meanwhile, several migrants swam around or climbed over the border barrier overnight and were detained by USA officials. Judge Jon Tigar rejected the Justice Department's request to suspend his earlier order temporarily blocking the ban.
The challenger was flat-out on the canvas but somehow found a way to not only recover to beat the count but also box the better of the two men down the stretch.
And to his credit, he almost did so in the 11th hour.
Fury who remains undefeated there are few questions arise here as to whether he's fully back to the form he showcased when he outpointed the longstanding reign of Wladimir Klitschko back in 2015.
"If Wilder loses he'd have to make a statement". "If this other promoter calls tomorrow like he said, we'll hear him out".
Those at ringside - who included boxing greats Floyd Mayweather, Evander Holyfield, Lennox Lewis and James "Buster" Douglas - and the rest of the world watching on were all astonished at how Fury managed to get up from seemingly looked like total knock out.
"I've always spoken that there should be one champion, one face, one name".
"I'm not sure the other side is still not afraid of him", opined Finkel.