Selectors named the 20-year-old Queensland opener Renshaw alongside two other batting debutants, Peter Handscomb and Nic Maddinson, in a 12-man squad.
Pacemen Chadd Sayers and Jackson Bird return to the national side, and Matthew Wade comes in as wicketkeeper after Peter Nevill was axed.
Australia last made as many as six changes in 1984, when they faced the then formidable West Indies. Joe Burns, Adam Voges, Callum Ferguson, Nevill and Joe Mennie paid the price for Australia's wretched innings and 80-run defeat to South Africa in last week's second Hobart Test.
The dramatic team overhaul follows Australia's heavy defeat to the Proteas in Hobart to give the tourists an unassailable 2-0 lead in the series.
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South Africa could inflict the first home series whitewash in Australia's history if they win the pink ball final Test at the Adelaide Oval, starting on Thursday. Renshaw was born in Yorkshire and lived in England before coming to Australia at the age of 10.
"Matt has established himself in a short period of time as one of the best young opening bats in the country," Hohns said.
"His form is currently very good and we see him as a very exciting prospect for the future."
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Victorian batsman Handscomb, 25, is also the holder of a British passport, but was born in Australia to English parents. Handscomb scored 137 against South Africa A in Townsville and 87 against India A in Brisbane this year and hit an opportune 215 for Victoria in the latest round of the Sheffield Shield.
Maddinson, 24, became the youngest player to score a century on Sheffield Shield debut for New South Wales when he was 18 in 2010 and has also represented Australia in Twenty20 cricket.
"Nic is an exciting and talented young player and we feel now is the ideal time for him to be involved with the Australian team," Hohns said.
Sayers, an Adelaide Oval specialist, had been in Australia's Test squad earlier this year but did not play.
"We consider Chadd and Jackson to be very good bowlers that also can bowl a large amount of overs in conjunction with Mitchell Starc and Josh Hazlewood," Hohns said.
"Chadd bowls very well in Adelaide and Jackson is coming off a strong performance in his last Test match earlier in the year and both deserve their chance."
There may have been a seventh change if not for a calf injury to the left-arm spinner Steve O'Keefe, who had been favoured to oust the Nathan Lyon.
Lyon, Australia's all-time leading off-spinner with 213 Test wickets, has taken just two wickets against South Africa at 120.50 each.