In a sloppy contest in windy conditions, the inaccurate Demons edged away from the Giants after quarter-time to win 11.18 (84) to 9.5 (59).
Melbourne restricted the Giants to just four goals in the opening three quarters before the home team booted five in the last term.
The victory means Melbourne will almost certainly avoid the wooden spoon, with the Demons now two wins above Gold Coast and the Giants, who are last.
The Giants' percentage is vastly inferior to the Suns, meaning GWS will need to spring an upset in the final two rounds of the year to avoid the wooden spoon.
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Luke Power became the 66th man in VFL/AFL history to reach the 300-game milestone, but his side couldn't rise to the occasion.
The Giants trailed by only two points when young gun Toby Greene goalled in the fifth minute of the second quarter.
Unfortunately for most of the crowd of 7,561, the hosts' next goal would come in the sixth minute of the last term through key defender Phil Davis.
This was a clash between two sides anchored to the bottom quarter of the ladder, and in many ways it showed.
Turnovers resulted in goals - or behinds more commonly - and too many passes failed to hit their target.
But it was a match with no shortage of feeling - Melbourne's Sam Blease went for Sam Darley's jugular in arguably the most heated of a series of spot fires.
It was the sort of spirit the game was played in, with both sides playing for pride rather than draft picks as the Demons have been accused of doing in past seasons by former teammate Brock McLean.
And there were some highlights - Melbourne's Jeremy Howe flew for marks in his normal style and clutched a screamer in the third term.
Demons co-captain Jack Trengove had an outstanding game while Greene showed incredible attack on the ball and football smarts.
In one passage of play on the wing, the 18-year-old grubbered to himself and produced a bullet-like pass into the forward 50m.
The Giants' endeavour was never lacking, but the same couldn't said of their discipline and decision-making.
The conditions didn't help.
While the snow that GWS coach Kevin Sheedy said pre-match he was hoping for failed to eventuate, a strong wind made the goalposts sway for most of the game.
However, not all of the side's struggles could be blamed on the gusts.
Israel Folau, devoid of even a skerrick of confidence, struggled to make an impact.
The former NRL star was shifted to defence in the last term, where he collected his first kick which was greeted with bronx cheers from the fans.
GWS midfielder Taylor Adams sustained a wrist injury late in first half but played through the pain, while Demon Jack Watts successfully returned from an ankle injury as the substitute.
It was Melbourne coach Mark Neeld's first away win.
GREATER WESTERN SYDNEY 2.2 4.4 4.5 9.5 (59)
MELBOURNE 3.4 6.10 9.13 11.18 (84)
BEST
GREATER WESTERN SYDNEY: Greene, Giles, Power, Adams, Phillips
MELBOURNE: Dunn, Grimes, Howe, Trengove, MacDonald
GOALS
GREATER WESTERN SYDNEY: Greene (2), Giles, Power, Adams, Phillips, McDonald, Smith, Davis
MELBOURNE: Howe (3), Sellar (2), Trengove (2), Rivers (2), Green, Grimes
INJURIES
Melbourne: Nil
Greater Western Sydney: Nil
SUBSTITUTES
Melbourne: Jack Watts replaced Tom Couch in the third quarter
Greater Western Sydney: Steve Clifton replaced Will Hoskin-Elliott at three quarter-time
Reports: Nil
Umpires: Ryan, Armstrong, Harris
Official crowd: 7,561 at Manuka Oval
The views in this article are those of the author and not necessarily those of the AFL or its clubs.
