Two of the three ringside judges scored the fight 115-113 and 116-112 to Beterbiev while the other called it tied at 114-114.
Both men were previously undefeated before the fight in Riyadh, with Bivol holding the WBA belt and Beterbiev the reigning WBC, WBO and IBF champion.
By taking the bearded Beterbiev to a full 12 rounds at the Saudi capital's Kingdom Arena, Bivol became the first man to go the distance against a champion with a previous 100% record of winning by knockout or stoppage.
"I wanted to box more, I don't like this fight. I was a little bit uncomfortable," said Beterbiev.
"I felt uncomfortable, because usually I'm not waiting for the bell."
The headline clash, postponed from last June after Montreal-based Beterbiev suffered a knee injury, put the four recognised major belts in the hands of one man for the first time.
The last undisputed light-heavyweight champion was American Roy Jones Jr. who beat Reggie Johnson to unify the WBA, WBC and IBF belts in 1999.
Bivol made himself a moving target in a high-quality fight between the big punching and aggressive Beterbiev and a more fluid rival who landed eye-catching early blows and had the better of the early rounds.
There was little between the two at the halfway point, with Beterbiev possibly behind but every round was a close call in a fight short of fireworks but with plenty for the purists.
Beterbiev knew he had to close with a bang in the last two rounds and raised the tempo but Bivol hung in there and fired back some powerful combinations.
"I just congratulate Artur and his team, he deserves it," said Bivol, looking forward also to a possible rematch.
"I did my job, I felt I could do better, I always feel I can do better, but that's the opinion of the judges. He won."
Australia's Jai Opetaia earlier retained his IBF cruiserweight world title when Jack Massey's corner threw in the towel two minutes into the sixth round with the beaten Briton bleeding from a cut to the side of his nose.
The convincing win took Opetaia's record to 26-0.
Unbeaten Australian Skye Nicolson won the first women's world title fight held in Saudi Arabia when she defended her WBC featherweight belt against Britain's Raven Chapman in a unanimous points decision.
A light-heavyweight fight between Britons Ben Whittaker and Liam Cameron ended in a draw after both crashed out of the ring, while Fabio Wardley stopped Frazer Clarke in the first round of their British heavyweight title fight.
