It took Cooper seven second-half minutes to complete his hat-trick as the Australians cut loose, running in 11 tries at Wellington Regional Stadium to get their World Cup campaign back on track.
It was a much-needed, confidence-boosting display by Robbie Deans' side who were determined to bounce back from the disappointing performance against Ireland.
But it came at a possible cost with Pat McCabe forced from the field with a possible shoulder injury and Anthony Fainga'a knocked out cold in the closing seconds of the match and taken off on a stretcher.
Australia led 22-5 at half-time thanks to tries by Rob Horne, Rocky Elsom, Kurtley Beale and Fainga'a.
Drew Mitchell and McCabe got the scoring underway after the break before Ashley-Cooper's triple burst. Fainga'a grabbed his second and Radike Samo rounded off the rout.
But goal-kicking remained a problem until Berrick Barnes was brought on for Beale just before the break. He kicked four of his five attempts while Cooper converted just two from five and Beale missed with his only shot.
The Eagles No.8 JJ Gagiano got a well-deserved try midway through the first half, but Blaine Scully had his match ended early when he was sent to a sinbin for a professional foul in the 75th minute, not that it affected the outcome as the match was well and truly over by then.
The Wallabies looked nervous in the opening minutes with Cooper shelling a pass then throwing to no-one as Mitchell over-ran.
But two tries in three minutes settled the nerves as Horne, back in the side after an elbow injury, then Elsom made the USA pay for some poor defending.
But having looked set to run riot, the Wallabies found themselves having to defend furiously on their own line after Eagles stand-in captain Tim Usasz darted through a huge gap to take play deep into the Wallabies half.
After hammering away at the Wallabies line the try eventually came in the 23rd minute when Gagiano showed good strength to pick up off the back of a retreating USA scrum to get round Elsom and score in the corner.
But it was one-way traffic after that as the USA, who showed 14 changes from the team that started in the win against Russia, missed tackles or committed unforced errors.
Eagles winger Kevin Swiryn lost the ball forward just short of the Australian try-line and Beale finished at the other end in the 31st minute.
Then a great line-break by Horne set up the bonus-point try for Fainga'a five minutes before the break.
The tries just kept coming early in the second half as Robbie Deans turned to his bench bringing on Samo for Elsom, McCabe for Horne, then Dan Vickerman for Palu.
Mitchell was over in the 45th minute and then McCabe, who had only been on the pitch a minute, scored the Wallabies' sixth four minutes later.
Ashley-Cooper was virtually untouched as he ran in his three tries before Fainga'a and Samo added the finishing touches.