The hard-hitting Wilder knocked Fury down twice, including a brutal right-left combination that sent the towering Fury to the canvas in the 12th in what initially looked to be the end of the fight.
But the 'Gypsy King' willed himself to his feet and held on to send the fight to the judges, who rewarded him for controlling much of the fight behind his long jab, precise footwork and slippery defence.
One judge scored the fight 115-111 to Wilder, another 114-112 to Fury and the third had it 113-113.
The scorecards showed that Wilder benefited greatly from his two knockdowns in the ninth and the 12th, which all three judges scored 10-8 in favour of the champion. In all the other rounds the fighters were separated by a single point.
Wilder said he thought the battle was over when he saw Fury's eyes "roll into the back of his head" as he fell hard on his back early in the 12th round.
Wilder at first celebrated with a shimmy only to appear stunned when Fury beat the count and got back on his feet.
Both fighters preserved their unbeaten records with the draw, but both thought they had done enough to earn the victory in the bout, which played out before 17,698 fans in downtown Los Angeles.
"I think with the two knockdowns I definitely won the fight," said Wilder (40-0-1), adding that he started slow and rushed his punches in a sub-par performance.
"We poured our hearts out tonight. We're both warriors but with those two drops I think I won the fight," he said in the ring after the fight.
"When I rush my punches like that I'm never accurate.
"The rematch I guarantee I'm going to get him."
FURY'S REDEMPTION
Former world champion Fury (27-0-1), in just his third bout since a two-and-a-half year absence from the sport following mental health issues and a failed drug test, was convinced he should have walked away with the title.
"We're on away soil, I got knocked down twice, but I still believe I won that fight," said Fury, who out-landed Wilder 84-71 overall.
"That man is a fearsome puncher and I was able to avoid that.
"The world knows I won the fight."
After exchanging harsh words in the leadup to the fight, both men were full of praise for each other following the final bell and were eager for a rematch.
"One hundred percent we'll do the rematch," Fury said.
Fury also taunted Anthony Joshua, the undefeated holder of the WBA, IBF, WBO and IBO crowns, from the ring.
"We are two great champions," he said. "Me and this man are the two best heavyweights on the planet."
A win for Wilder would have likely set up a blockbuster world heavyweight unification title bout next year against the 22-0 Briton, a fight the American has long sought.
But in the widely expected rematch with Fury, the 33-year-old 'Bronze Bomber' will likely need to win to get his shot.
(Editing by Peter Rutherford/Sudipto Ganguly)
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