The tourists made an ominous start, conceding two early penalties and a goal-line drop-out before having a serious look at their hosts' try line.
Australia also had a claim for a penalty try after centre Atkins tackled his opposite number Tate a fraction early but video referee Steve Clark gave England the benefit of the doubt.
But it only delayed the inevitable and England were behind as early as the fifth minute.
Uncharacteristic errors cost us - McNamara
It came from Aussie second row Lewis, who took advantage of some slack defence, to burst through England's defensive line and cross unchallenged from close range.
But England's response was almost instant with Burgess barging his way through in what was their first attack of the game.
A conversion from Ben Westwood followed as did a penalty with England taking a surprise 8-6 lead.
But a series of errors and missed tackles followed and the Australians took advantage to open an 18-point lead at the break.
England first failed to deal with a kick that bounced around their in-goal area and which Lewis eventually grounded before Tom Briscoe's fumble handed Slater an opportunity to ground in the corner for Australia.
Win fails to cheer Aussie coach
Further poor handling from England saw Atkins' fumble punished by Tate before hesitancy by the away defence saw Tonga slide over for Australia's fifth try of the half.
But despite looking shell-shocked at the break, England made the perfect start to the second half with Robinson sliding over under the posts for their second converted try.
Any thoughts of a comeback were put to bed soon after though with Tuqiri going over in the corner, although England had reason to question an earlier forward pass in the build-up to the try.
Smith added a further penalty for Australia as torrential rain made handling difficult and slowed the pace of the game, but to their credit England kept going and Shaun Lunt came within centimetres of scoring on his debut.
England had further opportunities to add to their score but brilliant Australia defence kept them at bay.
England: S Tomkins (Wigan); D Goulding (Wigan), L Cudjoe (Huddersfield), R Atkins (Warrington), T Briscoe (Hull); S O'Loughlin (Wigan), L Robinson(Huddersfield); J Graham (St Helens, capt), J Roby (St Helens), S Burgess (South Sydney), G Ellis (Wests Tigers), J Tomkins (Wigan), B Westwood (Warrington). Subs: S Lunt (Huddersfield), S Fielden (Wigan), E Crabtree (Huddersfield), B Harrison (Warrington).
Australia: B Slater (Melbourne); B Morris (St George Illawarra), B Tate (NZ Warriors), W Tonga (North Queensland), L Tuqiri (Wests Tigers); D Lockyer (Brisbane, capt), C Cronk (Melbourne); N Myles (Sydney Roosters), C Smith (Melbourne), P Civoniceva (Penrith), L Lewis (Penrith), S Thaiday (Brisbane), P Gallen (Cronulla). Subs: D Shillington (Canberra), T Learoyd-Lars (Canberra), A Watmough (Manly), K Gidley (Newcastle).
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