The former heavyweight world title challenger from Tulsa, Oklahoma, built a 20-0 record to earn his shot at WBA champion Mike Weaver in 1981, but was beaten on points.
As he tried to rebuild for another championship opportunity, Tillis took on an ageing legend in Shavers.
Shavers twice challenged for the heavyweight world title in the 1970s as he took on Muhammad Ali and Larry Holmes, leaving a distinct impression on Ali with his punching power.
The Greatest famously reflected after their fight: “Earnie hit me so hard, it shook my kinfolk back in Africa.”
When he met Tillis, Shavers was 37 years old but still carried his astonishing power as he bludgeoned him face down in round nine.
To his credit, Tillis impressively climbed off the canvas to win a ten-round unanimous decision, however, he was then stopped three times between 1982 and 1983 by Pinklon Thomas, Greg Page and Tim Witherspoon.
This led to him losing his contender status and he instead became something of a gatekeeper.
In the space of 18 months between 1984 and 1986, he lost five times in six fights.
The last of these came against Tyson, who was a 19-year-old 19-0 (19 KOs) wrecking machine at the time, clearly on course for superstardom.
Tillis was expected to fall just like all of Iron Mike’s other opponents, however he stubbornly refused to do so.
Addressing a stamina issue that had seen him knocked out multiple times previously, Tillis was provided with a new diet by a doctor who identified that he’d been allergic to some of the food he’d been eating.
As a result, he was rejuvenated prior to his May 1986 meeting with Tyson and provided the youngster with a tough task.
Tillis took Tyson’s hardest punches, stood up to them, and fired back with his own.
Even when knocked down in round four, he was up at the count of two and battled through all the way to the final bell.
When the decision was read out, Tillis was only a narrow loser on two of the judges’ scorecards, while one had it wider.
Tyson would go on to become the youngest heavyweight world champion in boxing history later that same year, winning the WBC belt with a stunning knockout.
Later in his career, Tillis also provided tests for Frank Bruno, Evander Holyfield and Tommy Morrison, building a remarkable résumé of elite heavyweight opponents.
The two that he gets asked about the most though are the power punchers Tyson and Shavers.
Years later, Tillis told Boxing News 24/7: “People ask me about Tyson and Shavers – let me tell you, there’s no comparison. None whatsoever.
“Shavers, he hit so hard he could turn horse p*** into gasoline. He hit so hard he could bring back tomorrow.
“Tyson hit like a sissy in comparison.
“I beat Shavers, and I know I beat Tyson. I wanted a rematch with Tyson real bad, but Shavers? No way.
“When he hit me and knocked me down, I saw pink mice and rats smoking cigarettes.
“That fight was the toughest 30 minutes of my life. The Acorn was one bad dude, let me tell you.
“Against Tyson, with my new diet, I didn’t get tired and that boy was in trouble. He never would give me a rematch.”