The Kangaroos ran in eight tries in the first half, with Morris recording his hat-trick inside half an hour. They continued their impressive defensive effort which has seen them concede no tries in the three matches since playing England in the tournament opener.
This game was all about the surprise versus the expected; the debut nation USA riddled with part-time players, against the most successful nation in World Cup history, Australia, and their all-star line-up.
The luck seemed to be with the tournament favourites early on, as Cameron Smiths kick-off struck the right upright and rebounded to a green and gold shirt. The USA did well not to concede a try from the games first set.
However the Kangaroos only had to wait until their second set to record the first of their 12 tries, as Greg Inglis, playing at centre, fed Hayne who had no trouble touching down and setting the tone for the afternoon.
The USA came into their historic quarter-final looking to regain the momentum that had seen them reach the last eight with wins over the Cook Islands and Wales, following defeat in their final group game against Scotland in Salford.
Australia, meanwhile, were simply looking to maintain their 100 per cent record at RLWC2013, following their wins over England, Fiji and Ireland.
Despite this early set back the USA, through their own sprinkling of NRL talent, fought back, gaining valuable territory through Clint Newton, and came close to a try of their own but captain Joseph Paulo failed to connect with an attempted grubber to the line.
The spirit and determination of the American side was as evident as it has been throughout the tournament and was epitomised by Bureta Faraimos huge tackle on Billy Slater, which brought a cheer from Wrexham crowd, but it did not prevent Greg Inglis from ultimately going over for Australias second of the match at the end of the move.
Less than a minute after Johnathan Thurstons impressive conversion, it looked for a split second as though Paulo was about to open the USA account when he charged down Cooper Cronks kick, though the Australian scrum-half managed to backtrack and snuff out the danger.
It was the last time the USA would spend attacking, as Australia completed the first period with panache, Morris soon stretching the Australian lead to 14 points with a powerful solo effort. He picked the ball up just inside the Tomahawks half and sprinted down the wing.
It seemed to click the Kangaroos into gear, as Hayne, scorer of the games first try, jinked between two white USA shirts and used his power to ride two tackles, before offloading to enable Smith to cross.
There was a repeat almost straight from the restart, as Hayne did the early hard work and offloaded to Slater this time, who found the overlapping Morris free on his right to run in his second of the match. Smith then set up another try, putting in Cronk for his first of the afternoon as Australia, followingThurstons third goal, made it a point a minute after the first half hour.
Morris completed his hat-trick in the 35th minute after Inglis offloaded to his wing and then Cronks kick found Morris again. He plucked the ball from the air to record his fourth try of the first half.
The second period started worryingly for Australia, as Slater was forced off the field, helped by two physiotherapists with suspected damaged ankle ligaments.
The scoring followed the same pattern as the first half, as Inglis recorded his second of the afternoon with a show of strength, marching over the line with four Tomahawks clamped around his body.
Hayne then became the third Australian to score multiple tries, as Morris broke through the USAs defence and cut inside, only to reverse-pass to the Kangaroos number three, who had overlapped on the wing. Thurston converted to bring up Australias half century in under an hour.
With a little over 10 minutes remaining, Hayne went over for his own hat-trick after Australia won a penalty 20 metres from the USA line.
There was a brief moment when it looked as though the USAs extraordinary RLWC2013 journey could end with a historic try against Australia. Referee Henry Perenara asked for the video referees assistance with the Tomahawks stuck on the Kangaroos line, but he ruled out a touchdown.
Instead Australia swept up to the other end and rounded off their impressive display as Hayne claimed his fourth, knocking flat USA full-back Kristian Freed on his way to scoring in the last move of the game.
1 Billy Slater
2 Brett Morris
3 Jarryd Hayne
4 Greg Inglis
5 Darius Boyd
6 Johnathan Thurston
7 Cooper Cronk
8 Matthew Scott
9 Cameron Smith
10 James Tamou
11 Greg Bird
12 Sam Thaiday
13 Paul Gallen
14 Daly Cherry-Evans
15 Josh Papalii
16 Andrew Fifita
17 Corey Parker
1 Kristian Freed
2 Bureta Faraimo
3 Taylor Welch
4 Michael Garvey
5 Matthew Petersen
6 Joseph Paulo
7 Craig Preistly
8 Mark Offerdahl
9 Haveatama Luani
10 Eddy Pettybourne
11 Clint Newton
12 Matthew Shipway
13 Daniel Howard
14 Tuisegasega Samoa
15 Roman Hifo
16 Mark Cantoni
17 Les Soloai
Australia: 62 Tries: Hayne (4), Inglis (2), Morris (4), Smith, Cronk Goals: Thurston (6)
Referee: Henry Perenara
Touch-judges: Jose Periera and Tim Roby
Video referee: Phil Bentham