Tries for Freddie Steward and Jamie Blamire and the pinpoint goalkicking of Owen Farrell and Marcus Smith settled a penalty-ridden game.
England made most of the running in the first half and scored a superb try through fullback Steward after seven minutes but as both teams conceded a succession of penalties, Farrell and James O'Connor punished each other from the tee to keep it tight at 16-12 at halftime.
The ragged, indisciplined nature continued in the second half.
Australia were hit with two yellow cards in the game - with neither side really threatening the tryline but England still in the ascendancy.
Farrell, winning his 100th cap for England and the Lions, went off injured after landing five penalties and a conversion but Smith added another penalty to stretch the lead before replacement hooker Blamire sent the home fans wild when he galloped in from 60 metres in the final minute.
England have now won all eight of their games against the Wallabies, who conceded 18 penalties, since they lost to them in the pool phase to be knocked out of the 2015 World Cup.
"We stuck at it," said coach Eddie Jones. "We've had a tough week. Two COVID, Kyle Sinckler was injured in the first 10 minutes of the match - he was incapacitated.
"Australia have been in a bubble since June, so congrats to them for staying in it."
After thumping Tonga last week, England complete their end of year campaign against South Africa while Australia, beaten by Scotland and struggling to overcome some big-name absences, play Wales, both next weekend.
"It's the final game and we want to go into the Six Nations with a South African scalp," said Jones.