Chasing 301 for victory, Australia looked down and out at 244-9 with six overs remaining.
But Faulkner had other ideas as he launched an all-out assault on the English attack, being particularly brutal to Ben Stokes, who went for 1-74 from his 10 overs.
Faulkner smashed three fours and five sixes against England, who had been on track to record their first win over Australia on a miserable tour.
The Tasmanian sent the crowd of just over 32,000 into raptures with two massive sixes in the 49th over, before finishing England with three consecutive boundaries off Tim Bresnan to give Australia a 2-0 lead in the five match series.
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After starting cautiously, the left-handed Morgan picked up the pace in the last 10 overs, smashing four boundaries and clearing the rope six times in a brutal display, his second 50 taking just 24 balls.
With such an imposing target to chase, the Australians needed to get away to a good start -- but they were rocked early when Chris Jordan dismissed Aaron Finch, the first match century-maker spooning a simple catch to Gary Ballance at mid-off for a duck.
Part-time off spinner Joe Root then grabbed the key wickets of Michael Clarke (17) and Shaun Marsh (55) to put the visitors in control at 114-4.