Tries from prop Dan Cole, fullback Mike Brown, number eight Billy Vunipola and replacement hooker Jamie George combined with 24 points from the boot of flyhalf Owen Farrell extended their winning streak under coach Eddie Jones to nine matches.
Wingers Dane Haylett-Petty and Taqele Naiyaravoro, flyhalf Bernard Foley, fullback Israel Folau and flanker Michael Hooper crossed for Australia but they were unable to match the discipline and set-piece strength of the Six Nations champions.
England won the first Test in Brisbane 39-28 with their previous record points tally against the Wallabies before securing their first series triumph in Australia with a 23-7 victory in Melbourne on the back of huge defensive effort.
The tourists showed they had come to play running rugby on Saturday with some sharp early phases and they scored first when, after a burst for the line from Mako Vunipola, scrumhalf Ben Youngs fed his other prop Cole for the opening try.
Australia responded almost immediately through their backs, Folau feeding Matt Toomua for a dash down the touchline with the centre's pass inside setting up Foley to touch down.
Eight minutes later and Australia were in front, quick ball from a ruck in front of the posts allowing the Wallabies to move the ball down the backline for Haylett-Petty to cross in the corner.
Farrell and Foley traded penalties before England scored their second try on the half-hour mark when Brown chased down winger Anthony Watson's deft chip through.
The England flyhalf converted to put England back in front at 17-15 but Foley's second penalty on the stroke of halftime gave the hosts an 18-17 lead.
Flanker Chris Robshaw almost gave England the perfect start to the second half when he snared an errant Wallabies lineout and crashed over the line, only to be held up in goal.
Billy Vunipola peeled off the ensuing five-metre scrum to touch down, however, and the England pack stole Australia's next lineout before rumbling up the park and winning a penalty, which Farrell converted.
The tries kept coming with Hooper snaking his way to the line after 51 minutes and allowing Foley to level the scores at 25-25 with the conversion.
Farrell kicked his third penalty after a dominant England scrum to edge the visitors ahead but Toomua soon cut through the visitor's midfield and fed Folau for a score that restored Australia's lead.
A fourth Farrell penalty, from a scrum, made it again a one- point game before George shinned the ball over the line and touched down for England's fourth try and when his flyhalf kicked his fifth penalty, the visitors were 41-32 ahead with 13 minutes to go.
Another Farrell penalty extended England's record tally and cool game management kept the Australians pinned back until Naiyaravoro crashed over after the hooter for a consolation try.
Original source: England rack up record score to beat Australia 3-0