The 2015 World Cup group rivals produced a dismal spectacle for the opening QBE International at Twickenham, but the result was all that mattered to head coach Stuart Lancaster.
The autumn continues against Argentina next Saturday before concluding against a New Zealand team hell-bent on revenge after crashing to a record defeat last November.
Some notable victims feature among England's sequence of eight wins in nine matches - France, the All Blacks and now the Wallabies - and Robshaw hopes has demanded the run continues.
"We've come a long way in 12 months. This was time for us to kick on and start getting scalps like Australia's," the captain said.
"A lot of us in this group had never beaten Australia before, myself included. It's a great memento for us.
"First and foremost this was about getting the win. There was a bit of rustiness there but that performance stands us in good stead for Argentina.
"There was always going to be a bit of rust there and that game was exactly what was needed.
"Many of us had played in big Heineken Cup games recently, but we wanted to step up a gear because that what Test rugby is - it's about that intensity."
Character and an appetite for hard work underpinned England's first victory against Australia in two attempts under Lancaster after the Wallabies had triumphed 20-14 last autumn.
Maiden Test tries from Robshaw and Owen Farrell, who also kicked 10 points, demolished the 13-6 half-time deficit, although both scores were laced with controversy.
Outstanding full-back Mike Brown had both feet in touch before launching the counter-attack that preceded Robshaw's quick-witted touch down and Farrell clearly benefited from an obstruction by Dylan Hartley on Stephen Moore.
Australia, who have now lost eight of their 11 matches this year, were comprehensively outfought in the final half-hour and the way England ground out victory was admirable.
But they were alarmingly poor at times, particularly in midfield where the partnership of Billy Twelvetrees and Joel Tomkins failed to gel amid an incoherent three-quarter line that even Brown's masterclass was unable redeem.
Robshaw accepts there were shortcomings evident in the Cook Cup clash, but was delighted by England's spirit.
"The character of the squad was outstanding," Robshaw said.
"To come from seven points down against a very good Australia team who know how to score points... our defence was spot on.
"Besides their try I don't think they got in our 22 that often and that's down to our huge belief.
"It was about building pressure and momentum. We lost it in the latter parts of the first half. We talked about that at half time and came out all guns blazing.
"Our response to their try was exceptional. All the guys really put their hands up and wanted to give the crowd something to cheer about.
"We started quite well but lost a bit of momentum going into the second quarter."
Key to England's fightback was the temperament of Farrell, who missed three successive penalties but recovered to kick a penalty and two conversions.
The 22-year-old fly-half grew in stature in the final half-hour and his 58th-minute try, scored from a standing start, was well taken after he had spotted a gap between two forwards.
"That's the belief in of the guy. He's a credit to the squad and has that never-say-die attitude," Robshaw said.
"He took his try fantastically well. It was about building pressure at that stage.
"We'd managed to get some momentum and territory and it the end it told with his try."