The Demons opened up a staggering 86-9 halftime lead on Saturday afternoon, with veteran ruckman Max Gawn dominating an injury-hit Hawthorn.
However, the Hawks came to life midway through the third term, going on a run of 12 straight goals and threatening the unlikeliest of victories.
Hawthorn's Mabior Chol booted five goals in the streak, reducing the margin to 24 points with three minutes to go.
But Melbourne kicked the last two majors to claim a 19.11 (125) to 14.6 (90) win.
The victory was the Demons' first outside Melbourne under first-year coach Steven King and snapped Hawthorn's 12-game winning run at University of Tasmania Stadium.
"It's not an easy place to win. To walk away with four points and winning interstate … I'm just so happy with the way the boys set the tone early," King said.
"The last quarter we knew Hawthorn would come and have a run with it, (but) if you told me we'd win by 35 points, I'd take it."
Melbourne's Jacob van Rooyen and Bayley Fritsch both kicked five goals, while veteran Gawn was unstoppable in the ruck in the first half and picked off intercept marks.
Van Rooyen also had 24 possessions, five hit-outs and four clearances as Melbourne moved up to sixth and 10-6 for the season.
"One team had all their ducks in a row and came ready to play and one team didn't," Hawthorn coach Sam Mitchell said.
"We had problems in every department of the game and every phase.
"There are some of us that want to look at the second half, but we need to be realistic about where we were at.
"If you don't show up ready to play, you get taught a lesson, and we did."
The Hawks, who remain in third spot, were without a host of players, with Karl Amon, Ned Reeves and Nick Watson the most recent pre-game additions to the casualty list.
"We had some changes to the side that took us a little while to settle into," Mitchell said.
"We recognise we've got some work to do to be the best side in the competition, which is what we strive for. We're not there yet."
Melbourne came flying out of the blocks in a seven-goals-to-one first quarter against the sluggish Hawks.
The Demons had seven individual goal scorers for a 47-8 lead at the first break - their best opening quarter of the season and Hawthorn's worst.
The damage kept coming in the second term, with Melbourne notching a six-goals-to-none quarter - Hawthorn's solitary point came when William McCabe hit the post.
Fritsch increased his goal tally to four, while Harrison Petty got his second as Melbourne stretched their lead to 86-9 at the main break.
Van Rooyen surged in the third quarter with a brace of goals to help increase Melbourne's margin to 96 points midway through the term.
The Hawks' worst result in Launceston, a 75-point loss to St Kilda in 2017, appeared at risk, before they finally got something going.
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