The build-up to the match had been dominated by reports of internal tension and questions over England's form after a difficult year.
Senior players publicly backed Borthwick in the days before the match and their response on the pitch was emphatic.
A record points total against the Wallabies, achieved with physicality, ambition and far better discipline than earlier in the season, lifted England in the northern hemisphere standings and boosted confidence ahead of remaining fixtures against Japan and New Zealand.
England started with intent and an early Immanuel Feyi-Waboso try was ruled out for a forward pass, but the hosts were not denied for long. Jamie George finished a driven maul after eight minutes for the opening score.
Ollie Chessum added a second after strong work involving Feyi-Waboso, Henry Slade and George Furbank, and Joe Heyes claimed a third from another powerful maul while Australia prop Angus Bell was in the sin-bin for a hip-drop tackle.
Australia's only first-half response came on the stroke of half-time when Max Jorgensen intercepted a Jack van Poortvliet pass and raced clear.
Feyi-Waboso, who had been England's most dangerous attacker, did not reappear after half-time, and Henry Pollock was introduced on the wing, making an immediate impact.
Van Poortvliet atoned for his earlier error by scoring the bonus-point try early in the second half after a slick move involving Furbank and Tommy Freeman.
Pollock then struck twice in three minutes - once from a loose ball and once finishing a sharp handling move - to stretch the lead to 38-10.
Late consolation tries from Filipo Daugunu and Jeremy Williams reduced the deficit, but replacement scrum-half Ben Spencer sealed the victory with an interception try in the 76th minute.