Set 175 - the highest innings total of the rapid-fire fourth Ashes Test - England continued with their frenetic Bazball approach to blast their way to the target in just 32.2 overs.
Aggressive No.5 Harry Brook hit the winning runs late on Saturday, with wicketkeeper Jamie Smith at the other end.
It is the second two-day Test of the summer in a massive financial blow to Cricket Australia, after the series opener in Perth also ended with three days to spare.
This pitch was treacherous to bat on for both sides, prompting criticism even from fast-bowling greats such as Stuart Broad, Glenn McGrath and Brett Lee, and former England captain Michael Vaughan.
Kevin Pietersen, one of the heroes of England's famous 2005 Ashes triumph, described the match as "utter shambles".
Australia were skittled for 152 and 132, not even facing a combined 80 overs during their two innings as none of their batters reached 50.
England didn't even last 30 overs in their first innings on day one and were out for 110, trailing Australia by 42 runs.
It is the first time the same series has had multiple two-day Tests in 129 years.
Before this series, there had only been two two-day Tests in Australia - coming in 1931 and 2022.
It is England's first victory in Australia since they convincingly won the 2010-11 Ashes 3-1 - ending it with a heavy victory at the SCG, 5468 days ago.
The visitors travelled to Melbourne this week having lost 16 and drawn the other two of their 18 most recent Tests in Australia.
With hopes of regaining the Ashes already gone after defeats in Perth, Brisbane and Adelaide, this win salvages some pride for England and turns down the heat on coach Brendon McCullum.
England paceman Josh Tongue starred with seven wickets for the match, including 5-45 in the first innings.
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