Australia had led by as much as four goals in the last quarter and looked to have snapped the Roses' fierce resistance, but a handful of calamitous errors let them back into the contest.
Nigeria on Saturday won bronze in the women's 4x100m relay event of the Commonwealth Games.
It was the first time in six Commonwealth Games that neither Australia or New Zealand would take home the gold.
England, who avenged their bronze medal defeat to Jamaica in the semi-finals, came into the final as underdogs.
But third-ranked England upset the odds to claim victory over the favourites on a remarkable day of action.
England's men had won gold less than 20 minutes prior to the race, and a team of Asha Philip, Dina Asher-Smith, Bianca Williams and Lorraine Ugen ensured that they would also be standing atop the podium with a national-record time.
"We never got going", coach Lisa Alexander said.
"To be honest it was kind of all a blur".
"Every single box has been ticked".
"The girls have worked so hard over the last global phase", added Neville, the sister of former England worldwide footballers Gary and Phil.
'Australia are the renowned, world number ones and to beat them at that time, I'm really, really proud - the feeling of that is incredible'.
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