With the tourists seemingly poised for their first win over Australia this summer, Faulkner smashed 69 runs off just 47 balls to chase down England's 8-300 with one wicket and three balls to spare.
Australia appeared dead and buried when they lost Glenn Maxwell (54) and Ashes hero Brad Haddin (26) in the 35th over but with 30 needed off the final three overs, Faulkner launched an amazing display of hitting.
He belted consecutive sixes off Ben Stokes (1-74) in the 49th over and then smashed three fours in as many balls off the final Tim Bresnan over to get Australia home.
Faulkner and Clint McKay shared a 57-run last wicket stand, with McKay contributing two in what is the highest successful run chase in ODI history at the Brisbane venue.
"I knew I could do it deep down but it's always nice to get the boys over the line," Faulkner told the Nine Network.
The victory lifts Australia to a 2-0 lead in the five-game series.
Earlier, Eoin Morgan's blistering 106 off 99 balls had looked like being a matchwinning innings.
Morgan begun slowly but belted his final 50 off just 24 balls as he combined with young wicketkeeper-batsman Jos Buttler (49) in a 114-run, 68-delivery sixth-wicket stand which blew Australia away.
His sixth one-day hundred looked a long way off when he was caught at midwicket for one but then correctly pointed out to the umpires Michael Clarke's delivery was a no-ball because Australia had one fielder too many outside the circle for a powerplay over.
That reprieve granted, Morgan first re-constructed England's innings alongside Ian Bell (68) after they had lost three quick wickets and then delivered a stunning finish along with Buttler.
Australia's chase began shakily with both openers falling to one-handed catches.
Aaron Finch, a century-maker in Australia's game one victory, was snared by Gary Ballance off Chris Jordan's (2-53) bowling for a duck before Jordan took a sensational right-handed grab off his own bowling from a David Warner (18) drive.
When Joe Root (2-46) took the wickets of Michael Clarke (17) and Marsh (55), the hosts looked done but members of England's Test squad on the field must have feared the worst as Haddin combined with Glenn Maxwell to put on 80 in 66 balls.
But when both fell to Bresnan (2-64) the English could scent victory.
England captain Alastair Cook's roar when he snared the catch to dismiss Haddin said a lot about how his summer has gone but another devastating psychological blow was still to come from Tasmanian Faulkner.
The tourists have only one day to recover with the third game to be played in Sydney on Sunday and there will be doubt over Morgan's fitness after he limped off late in Australia's innings with a calf problem.
Australia captain Clarke hailed Faulkner as the nation's new "Michael Bevan" following his heroics and the 23-year-old said he'd revelled in the challenge of guiding his country home.
"The crowd was quite loud and I've been in that situation a fair few times being the all-rounder when you bat at the end and a lot of times I haven't been successful and I've stuffed up the game," he said.
"It was just nice to get the boys over the line this evening."
Faulkner said while Australia understood England's struggles there was still no sympathy for the tourists as they continue to hunt for their first international win on tour.
Morgan, who said both he and bowler Boyd Rankin (hamstring) will have to be assessed before Sunday's match, said there would be a challenge for England to rouse themselves at the SCG.
"It is quite tough," Morgan said.
"We were all over today's game. Did a lot of things right. We let a good side come in at the end and allowed them to play.
"We're as surprised as anybody at the result."