Eddie Jones urged England to claim a South African "scalp" after they warmed-up for next week's repeat of the 2019 World Cup final with a 32-15 victory over his native Australia at Twickenham.
England recorded their eighth successive win over the Wallabies since Jones took charge after a 2015 World Cup where they were knocked out by Australia.
A penalty-strewn encounter saw England score the only two tries of the match.
Full-back Freddie Steward crossed in just the seventh minute before Jamie Blamire went over in the last play of the game, with the replacement hooker now having scored in all four of his Test appearances.
England will now finish their 2021 season against South Africa, the team that beat them in the World Cup final in Japan two years ago, at Twickenham next week with the Springboks coming into the game on the back of a 30-15 win over Scotland at Murrayfield on Saturday.
"It's the final game and we want to go into the Six Nations with a South African scalp," said Jones.
England prevailed against Australia despite being without loosehead props Joe Marler and Ellis Genge after the pair tested positive for Covid-19 earlier in the week.
And they suffered further problems during the match itself with hooker Jamie George going off at half-time.
"We've had a fairly disrupted week," said Jones. "We have had two Covid positives and a young prop (Bevan Rodd) come in on Thursday. We lost Jamie George at half-time, Kyle Sinckler got a bad dead leg early in the first half so we had to battle today."
All the Wallabies' points came via five James O'Connor penalties, with Australia again lacking a cutting edge in the absence of Quade Cooper and Samu Kerevi after the backs opted against touring because of their Japanese club commitments.
"We predicted it would be more of a free-flowing game like Australia like to play but it turned out to be a penalty-heavy game, a lot of set-piece contests and kicking," said Jones.
This match saw fly-half Marcus Smith paired alongside England captain Owen Farrell at inside centre for the first time.
It was just Smith's third Test whereas Farrell was winning his 100th cap, a tally that includes six appearances for the British and Irish Lions.
But the duo still combined impressively before rising star Smith's delayed pass sent full-back Steward in for a seventh-minute try.
Farrell and Smith also kicked 22 points between them, with cricket fan Jones saying: "They are a bit like two opening batsmen who haven't batted together facing the new ball for the first time.
"Every time they bat together after this, they will be better.
"I thought the first try we scored is probably one of the best tries I've seen from an England side; our handling, our running lines, hitting the holes, it was absolutely outstanding and we want to do more of that."
Australia conceded 18 penalties to England's nine as they suffered a second successive defeat after a 15-13 loss to Scotland last week ended a five-match winning streak.
"We got hammered in the penalty count," said Australia coach Dave Rennie. "We just made too many errors and we gave away dumb penalties. It's frustrating."