A 33-13 win for the Wallabies four years ago ensured England suffered an embarrassing pool-stage exit at the World Cup on home soil and prompted the Rugby Football Union to hire Australian Eddie Jones as their new head coach.
Tasmanian Jones has had Cheika's number ever since, with England winning each of their six meetings between 2016 and 2018.
However, that record is not weighing on the mind of Cheika, who has already said he will walk away from his post if Australia do not win the World Cup.
"The fear inside us is dead," Cheika said at a news conference.
"We are not afraid to go there and get it. That means it will be a great game."
— Rugby World Cup (@rugbyworldcup) October 17, 2019
That attitude perhaps explains Cheika's decision to roll the dice on 19-year-old Jordan Petaia, who will become just the fourth teenager to appear in a World Cup knockout match when he starts at outside centre.
Petaia only made his Test debut in the pool stage and both his previous appearances came at wing, but he has been shifted inside with Reece Hodge returning from suspension.
"I trust him infinitely," Cheika added of Petaia.
"He's looking good as gold. It's going to be fast and aggressive but I just know he will rise to the challenge - I've seen it in him."
Jones has also taken a gamble, dropping the in-form George Ford for Henry Slade and switching captain Owen Farrell to fly-half.
England have won all three of their World Cup matches so far - with their game against France cancelled due to Typhoon Hagibis - and Jones knows they need to raise their level against the Wallabies.
"We've had three games, we've had three bonus-point wins, we can't do more than that," Jones said.
"Do we have to play better than that against Australia? The likelihood is yes, and we are prepared for that."
PLAYERS TO WATCH
England - Maro Itoje
Turnovers are key in such tight contests and no one won more than Itoje in the pool stage. The forward only played in two games and yet regained the ball on seven occasions.
— Maro Itoje (@maroitoje) October 5, 2019
Australia - Samu Kerevi
While Petaia will garner much of the attention, England must keep an eye on his midfield partner and Queensland Reds team-mate Kerevi. He beat 20 defenders across three appearances in the pool stage - the most of any centre - and more than England's top two players - Manu Tuilagi and Jonathan Joseph - combined.
Photo Getty Images Caption: Michael Cheika