Suaalii chased down another kick-off as Australia got the second half under way and England were drawn into a game of open spaces, long passages and frequent turnovers.
Australia thrived in the chaos.
Second row Jeremy Williams dived into the corner like a wing after 50 minutes to move his side 25-18 clear.
From the kick-off, Wright slit England open down the middle with a swerving run, and the scrambling hosts gave away a soft penalty as they tried to stem the attack.
Lolesio slotted to put Australia 10 points clear and, with little over 25 minutes left, England were staring down the barrel.
With a recent history of dismal final quarters, the prospect of an England comeback was not supported by the stats.
But the home crowd, as against Ireland in March, relished the chase and raised the volume.
Smith was the conductor at the centre of the maelstrom.
Sleightholme ate into the Wallabies’ lead, latching on to Smith’s smart kick to make it 28-23, before the Harlequins man, moved to full-back by the introduction of George Ford, dropped a shoulder and darted deep into Australia territory 10 minutes later.
Fast ball was fed to Alex Dombrandt, whose floated pass allowed Sleightholme a clear canter into the corner.
Smith landed the touchline conversion and, with 10 minutes to go, England led once more at 30-28.
They could not contain the Wallabies, though, with home errors breathing life into the opposition.
Andrew Kellaway streaked clear to score after the ball went to ground in a mess of an England midfield move.
Itoje’s score seemed to have salvaged victory, but England gave away possession off the kick-off and, with tired legs unable to cover ground, Jorgensen raced away for a gut-punch game-winning score.
