Young guns Freddie Steward and Marcus Smith scored the tries and England's streetwise pack bossed the breakdown as coach Eddie Jones masterminded a second series victory over his own country after the 3-0 sweep of 2016.
Australia scored tries through Tom Wright and Folau Fainga'a in front of a sellout crowd of 43,274 at the Sydney Cricket Ground but, for all their attacking brio, their accuracy deserted them too frequently at crucial moments.
"We had to fight like anything today, they were always going to throw it around so we had to defend well," Jones told reporters.
"This was tougher than 2016. We are nurturing this team on this tour. I'm really pleased with the development of this team, it's been outstanding."
Little had separated the sides over the series, with the Wallabies taking the opening test 30-28 in Perth and England striking back with a 25-17 victory in Brisbane last week.
After being blown away in the first half an hour in Brisbane last week, Australia had the better of the first half with some bright running but still managed to head back to the dressing room 11-10 down.
England's Owen Farrell had opened the scoring with a penalty after 17 minutes but the Wallabies soon responded with a fine try from winger Wright, who made a break down the right wing before exchanging passes with Nic White and touching down.
Australia flyhalf Noah Lolesio added the extras and a penalty on the half hour mark but Farrell almost immediately reduced the deficit with his second three-pointer.
Some ill-discipline from the Wallabies gifted England another penalty just before halftime and they kicked to touch, pounding away at the home defence until Steward managed to find a slim fissure in it to touch down in the left corner.
England returned after the break showing the same sort of physicality they had in Brisbane, and a third Farrell penalty and an opportunist try from Marcus Smith had them 21-10 in front after 55 minutes.
Lolesio had the ball batted out of his hands and Smith pounced on it to race away and score.
Australia knew the series was on the line and laid siege to the England line, finally getting their reward in the 66th minute when replacement hooker Fainga'a forced his way over to reduce the deficit to 21-17.
Roared on by the crowd, the Wallabies hammered away looking for a winning try but the England defence held firm to almost certainly secure their coach his job through to next year's World Cup.
"We created a lot of opportunities, we just weren't clinical enough," said Australia coach Dave Rennie, who was without 11 top players through injury or suspension.
"It was disappointing because at this level you've got to take your chances. It hurts."
