Tyson, who was fighting 15 years after his last professional outing, dominated for long periods at the Staples Center in Los Angeles.
Jones, 51, who only retired in 2018, was content to hold for the duration and rarely landed a blow on his 54-year-old opponent.
Tyson should have been given the nod by the three former world champion judges after eight two-minute rounds - but instead the fight was scored even.
Tyson said: "I'm good with that. I'm good with a draw because I entertained the crowd and the crowd was happy with it.
Mike Tyson and Roy Jones Jr in action (Image: Getty Images for Triller)
"I'm used to doing it for three minutes. I hope to go further, absolutely, and he can be on the card as well.
"I was very happy to be here, despite what everyone says I was happy to go to eight rounds.
"Nobody thought I could go eight rounds, but you've got to go the distance, that's boxing."
Tyson took the fight to Jones in the first round and the small ring played into his hands as he switched from head to body while Jones looked to hold.
Both men were breathing heavily after the opening salvo but Tyson continued to look the fresher in the second session as he landed his jab to the head and then followed up with a right hand.
Jones insisted on holding on in the third round as he smothered Tyson and prevented him getting his shots off. The fight resembled a hugging contest at times with Tyson the only one looking to land his shots in the fourth session.
Tyson was again the sharper in the fifth round as he landed a counter left hook as Jones was left breathless as he headed back to his corner.
The sixth round was instantly forgettable as Jones struggled with his fitness but Tyson was able to land to the body in the penultimate session.
Tyson connected to the body in the final round but Jones clung on to hear the bell before the decision was eventually announced.
Later it emerged Christy Martin gave Tyson the nod 79-73,Vinny Pazienza opted for Jones by a score of 80-76 while Chad Dawson scored it level at 76-76.
Both men seemed keen to fight on, whether against each other or against new opponents.
Jones said: "We've got to do this again. Everybody loves Mike; I love Mike too but it's something else taking punches from Mike.
Tyson and Jones Jr after their draw
"I'll go talk to my family, see how they feel about it and if they want to do it again, we'll do it again."
On the undercard, YouTube star Jake Paul delivered a sickening KO against former NBA star Nate Robinson.
Paul was fighting for the second time as a professional and dropped Robinson with his right hand.
And when he did so for a third time, the former basketball player was left face down on the canvas and in need of lengthy treatment.
Earlier, former two-weight world champion Badou Jack won every round against the tough but outclassed Blake McKernan.
There were also victories for the impressive Jamaine Ortiz who stopped Sulaiman Segawa and for Edward Vasquez who earned a split-decision win over Irvin Gonzalez.