Eddie Jones's side had been hoping to make the perfect start to the three-match series after losing successive fixtures against Ireland, France and Barbarians since the middle of March.
However, England could only fall to a disheartening result, despite Australia being reduced to 14 men when Darcy Swain was sent off for a headbutt in the first half.
There were times when England were temporarily reduced to 14 men, with Jonny Hill spending 10 minutes in the sin-bin for his part in the same incident and Billy Vunipola facing the same punishment with the score at 16-14 to Australia for use of his shoulder.
Nevertheless, England can have no arguments over the result, Australia progressing into next weekend's encounter in Brisbane with the opportunity to wrap up the series.
Before Swain's 34th-minute dismissal, the game had been lacking any real incident, England holding a 6-3 lead courtesy of two Owen Farrell penalties.
Despite being at a player disadvantage, Australia were 9-6 ahead by the 43th minute, but a try from Ellis Genge gave the visitors control of the contest.
𝐀𝐔𝐒𝐓𝐑𝐀𝐋𝐈𝐀 𝐓𝐑𝐘! 🇦🇺— Sky Sports Rugby Union (@SkySportsRugby) July 2, 2022
A beautifully timed pass sends Petaia through and he then battles through two English defenders to finish brilliantly! ⚡
Lolesio converts and Australia lead 16-14! #AUSvENG pic.twitter.com/NvNtGJoyrb
Sitting 11-9 ahead with 20 minutes remaining, England were in a position to see out the match, a sustained Australian comeback seemingly being out of the question.
However, Jordan Petaia and Folau Fainga'a touched down either side of Vunipola's sin-bin-worthy infringement, and a further try from Pete Semu effectively ended the game as a contest with two minutes left, the scoreline reading 30-14.
Completely against the run of play, England rallied with tries in the 80th and 83rd minute respectively, Henry Arundell and Jack van Poortvliet both getting on the scoresheet on their maiden appearances.
Regardless of England doubling their total during the closing embers of the game, the scoreline did not necessarily reflect how Jones's men were second best to a team who play 46 minutes of normal time a player light.
Jones and his squad are now left with the task of regrouping ahead of the next clash in Perth, a defeat in that fixture likely to lead to further question marks over Jones's long-term future as head coach.