Wilder (40-0-1, 39 KOs) knocked Fury (27-0-1, 19 KOs) down twice, including a brutal right-left combination in the 12th that initially looked like it would end the fight.
Fury, who somehow willed himself to his feet and held on to send the fight to the judges, had earlier controlled much of the bout 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.
WBC President Mauricio Sulaiman said the duo were a credit to boxing.
"I wish to once again congratulate Deontay Wilder and Tyson Fury for their great battle inside the ring and for the exemplary sportsmanship after the bout," he said.
Both fighters have spoken about their desire for a rematch, with Wilder reiterating that on a teleconference call on Tuesday.
"I'm willing and ready to give Fury the opportunity ASAP," Wilder said. "It's only right to give Fury a rematch as soon as possible.
"I'm ready whenever he's ready to do it. I'm ready to give the fans what they want to see and end this talk once and for all (about who won)."
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Peter Rutherford)
