Fresh from a two-week break after their round one win over Adelaide, the Bombers raced to a five-goal lead 23 minutes into the first quarter, were 102 points up by three-quarter time, and won 28.16 (184) to 5.6 (36).
James Hird's men won the inside-50 count 78 to 28.
It was Essendon's first win over Melbourne since round 12, 2009, and the victory emphatically snapped a three game losing streak against the Demons.
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It was also the Bombers' greatest winning margin against Melbourne, eclipsing their 122-point victory in round 15, 1986.
In stark contrast, Mark Neeld's embattled Demons team has lost its first two matches of the season by a combined total of 227 points.
Remarkably, Saturday night marked the Demons biggest loss at the MCG.
Dyson Heppell ran free all evening and was a dominant force for Essendon in the midfield. He gathered 23 possessions in the first half and finished with 36.
Jobe Watson (39 touches and three goals), David Zaharakis and Brent Stanton also won plenty of the ball, while star recruit Brendon Goddard's many classy contributions included a 50m goal from on the boundary line in the opening quarter.
Stewart Crameri led the way up forward for the Bombers with six goals, while Tom Bellchambers finished with four.
Down back, ageless warrior Dustin Fletcher halted many of the Demons' sporadic attacking moves.
Melbourne suffered its first blow in the hour before the game when Jordie McKenzie injured his calf during the warm-up.
He was replaced in the selected side by David Rodan, who became the sub, with Aaron Davey moving into the starting 21.
Despite that hiccup, the Demons began as if desperate to atone for their woeful performance against Port Adelaide in round one.
And their supporters had something to cheer about when Davey snapped an early goal and second-gamer Jack Viney took a great grab over Brent Stanton.
However, Neeld's men soon found themselves staring down an all too familiar scoreline.
Defender James Frawley was Melbourne's best player, while Jeremy Howe, Nathan Jones and co-captain Jack Grimes did their best to stem the tide.
Davey finished with two goals, including a brilliant dribbling effort in the second term, but such highlights were few and far between for a team bereft of confidence and hope.
Things get no easier for Melbourne in round three. The Demons host West Coast at the MCG next Saturday.
Essendon will face its toughest test of the season to date when it heads to Patersons Stadium to take on another unbeaten team, Fremantle, next Friday night.
ESSENDON 6.2 13.6 21.11 28.16 (184)
MELBOURNE 2.1 4.5 5.5 5.6 (36)
GOALS
Essendon: Crameri 6, Bellchambers 4, Watson 3, Davey 2, Heppell 2, Howlett 2, Merrett 2, Hurley 2, Stanton 2, Goddard, Ryder, Dempsey
Melbourne: Davey 2, Grimes, Clark, Jones
BEST
Essendon: Heppell, Watson, Bellchambers, Crameri, Goddard, Fletcher
Melbourne: Howe, Frawley, N Jones, Garland
INJURIES
Essendon: Nil
Melbourne: McKenzie (calf) replaced in selected side by Rodan
SUBSTITUTES
Essendon: Nick Kommer replaced David Zaharakis in the third quarter
Melbourne: David Rodan replaced Jack Watts in the third quarter
Reports: Nil
Umpires: Hosking, Kamolins, Wenn
Official crowd: 51,153 at the MCG
