Both Jack and opponent James DeGale suffered knockdowns in the action-packed title fight which ended in a draw after two judges scored it 113-113 and the other had it 114-112 in favour of DeGale, meaning neither will become unified super-middleweight champ.
The fighters retained their belts and each complained afterwards that they had won the fight at the Barclays Center arena.
World Boxing Council champion Jack was knocked down in the opening round when he got hit by a left hand. It was the third time he had been knocked down in his career, but he gained a measure of revenge by knocking out one of DeGale's teeth in the 10th round.
DeGale barely survived the final round when he was knocked down by a right uppercut on the chin. He managed to get up but threw very few punches during the rest of the 12th round.
"I thought I won the fight," said Sweden's Jack inside the ring immediately following the fight. "I finished stronger. His knockdown was a flash knockdown."
International Boxing Federation champ DeGale was standing next to Jack and had heard enough.
"Don't listen to this rubbish. I threw the cleanest shots," said DeGale, who is the first Briton to win both Olympic gold and a professional world title.
"I got huge respect for this man. He is tough, he's durable, he's skillful. You are the man. I won that fight."
DeGale said he felt those punches from Jack in the 12th. He managed to gather his senses and buy some time by getting into a clinch.
"I was kind of hurt. I am willing to do it again," DeGale said.
One of the strangest moments in a brutal, but thrilling, fight took place at the end the fifth round, when Jack accidentally punched Arthur Mercanti Jr., sending the referee staggering across the ring. Mercanti shook it off, took a couple of sips of water, and returned to action for the sixth round.
Jack's promoter Floyd Mayweather also complained about the scoring.
"This is the second time in a row Badou has gotten a bad decision," Mayweather said. "James DeGale is a hell of a fighter, but tonight he didn't win. At the end of the day, I don't know what the judges are looking at. This is bad for boxing."
Mayweather may win out in the end as the two will probably have to set up a rematch to determine who is the best 168-pound fighter in the world.
On the undercard, Gervonta Davis knocked out Jose Pedraza in the seventh round to capture the IBF junior lightweight title.
The 22-year-old Davis won his 17th straight fight with no losses with a dominating performance against the Puerto Rican, who was making the third defence of his title.