In the end, they couldn't decide, and the heavyweight world championship fight was ruled a split draw Saturday night at the Staples Center.
Lying helpless on the canvas, Fury looked concussed but, remarkably, Fury rose to beat the count and convinced referee Jack Reiss to let him continue.
Judge Alejandro Rochin, of Mexico, scored the fight 115-111 for Wilder, Canadian judge Robert Tapper had it 114-112 for Fury and British judge Phil Edwards had it 113-113 as both fighters remained unbeaten.
The 30-year-old "Gypsy King", who returned to boxing this year after missing more than two years through depression, drink and drug problems, had boxed cleverly to evade the heavy-hitting threat of Wilder for most of the fight.
"If it's a great fight and fans want to see the rematch then why not?"
The American champion struggled to connect cleanly with Fury throughout an absorbing contest, all too often sending huge arcing haymakers whistling past Fury's head.
Wilder almost stopped Fury 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 is likely to see a sequel. Wilder tried going to the body too but, more often than not, his punches landed harmlessly on Fury's massive elbows.
Fury had his best offensive round in the seventh, landing multiple left jab, right hand combinations that caused substantial swelling on Wilder's face.
But Fury gradually grew in confidence, regularly taunting Wilder by throwing his arms up in the air or behind his back.
Within minutes of the fight's conclusion being reached, people were comparing Fury's bounce back from the canvas to The Undertaker's famous recovery tactic of appearing to be knocked clean out, before sitting ominously back up as his opponent celebrated.