History maker Lucas Browne craves more fame and bigger pay days after becoming Australia's first-ever heavyweight boxing world champion with a stirring Rocky-type comeback effort.

Cut and knocked down in the sixth round, Browne dug deep to score a dramatic 10th-round stoppage of WBA regular heavyweight world champion Ruslan Chagaev in Grozny, Chechnya on Saturday.

The underdog's heroic comeback evoked memories of Jeff Harding's legendary last-round stoppage of WBC light heavyweight Dennis Andries in Atlantic City in 1989 and restored pride and respect to Australian boxing after a humiliating string of big-fight stoppages over the past two years.

The challenger barely survived Chagaev's follow-up onslaught in the last minute of the sixth round after he was dropped by a left hand.

"I know I've got a good chin. I obviously got rocked by something silly with his left hand, but I think I came back quite well," Browne told AAP.

The 36-year-old Sydneysider, who jabbed and moved well in the early stages of the fight, regained his composure and started his fightback in the seventh round, landing several jolting right uppercuts.

He was almost certainly still behind on the cards going into the 10th round, but poleaxed the 37-year-old Uzbekistan-born southpaw with a huge right-hand punch.

A clearly stunned Chagaev got to his feet, but sensing an opportunity to finish the fight, Browne capitalised.

He landed several more right-hand shots to Chagaev's head, prompting experienced South African referee Stanley Christodoulou to stop the fight.

"Rocky is a movie, but that was a real-life Rocky moment," Browne's manager Matt Clarke told AAP.

"He was trailing in the fight, that was clearly obvious.

"We asked him to dig deep and pull something out and he did."

Promoted by Britain's former two-division world champion Ricky Hatton, Browne is now poised to take advantage of his new lofty status.

"It (the win) does really put the cherry on top," said Browne, who will get his title belt later.

"It moves me into better positions for bigger fights, bigger money fights.

"But also just the history factor, it makes me proud of being Australian."

Browne now holds a portion of the WBA heavyweight title, which is currently split three ways, with a unified world champion in Tyson Fury and an interim belt holder in Luis Ortiz.

The win effectively takes him through to the semi-final of the tournament to produce one champion, with his next fight expected to be to be against Puerto Rican Fres Oquendo, who hasn't fought since dropping a majority decision to Chagaev in Grozny July 2014.

Clarke is hoping that fight could be held in Australia.

"I hope it's in Australia. If the Australian public don't support Lucas now, they never will," Clarke said.

"That win tonight is up there with every single greatest win ever by an Australian (boxer)."

Browne improved his unbeaten record to 24-0, including 21 knockouts, and Chagaev dropped to 34-3-1.

The Australian, who enjoyed a 16cm height advantage, showed he was much more than a big puncher as he delivered on his pre-fight promise to box and move.

He pinged the champion with jabs through the early rounds and landed the occasional right hand.

Chagaev worked his way into the fight and appeared to be getting on top through the middle rounds, landing some good shots to the body and tagging Browne with some good left hands.