The Eagles' 10.15 (75) to 6.10 (46) win was orchestrated in the second half after they strung together five goals and held the Demons to just one.
It is the first time the Eagles have won at the MCG since round five, 2007, and their first set of consecutive wins this season.
West Coast coach John Worsfold said it was pleasing for his young side to secure a win on the road.
"You love coming to the MCG to play but travel is one of the things we want our team to learn about as a young group," he said.
"We had a few players playing their first games on the MCG today, their first trip with the side, so there's a lot to gain from it."
Saturday was also the first time top youngsters Jack Watts and Nic Naitanui appeared on the same field since they were drafted in 2008.
Melbourne's Watts, in his fourth game and first for the year, started at centre half-forward while Naitanui lined up in the Eagles' attack with Dean Cox manning the ruck.
Neither had a huge impact in the first term as both sides struggled to hold the ball inside their forward arcs.
However, they showed their talent in the second with Watts taking a strong contested mark against Will Schofield and Naitanui leaping above Cameron Bruce to land a screamer.
Melbourne coach Dean Bailey said Watts, who ended with 15 touches, five marks and two scoring assists, would be considered to back up against Port Adelaide in Darwin next week.
"Jack took a couple of nice marks but it didn't matter who played in our forward line today," he said.
"The way we moved the footy would have been tough for many of our blokes in the forward line."
Josh Kennedy opened the game with back-to-back examples of his impressive ability to convert from all angle but the match quickly degenerated into a defensive struggle.
The first half became a low-scoring affair with just 10 goals kicked between the two sides. After the Eagles got 17 points clear, the Demons fought to level the scores by the main break.
The experienced heads at Melbourne in Bruce, James McDonald and Brent Moloney were driving the Dees while Mark LeCras was presenting well and Matt Priddis was important at the stoppages.
Both sides had injury concerns with Matthew Bate hurting an ankle, Aaron Davey groggy after face planting in the forward pocket and Kennedy battling illness and a sore head.
All three returned but the Melbourne pair was limited. Bate ended with 0.3 and Davey finished with 15 touches and no goals.
The Eagles edged in front in the third quarter and took a 12-point lead into the final term after a late goal to Matt Rosa.
Another to LeCras two minutes in sealed the result, despite the Eagles' best attempts to kick themselves out of contention with a string of six behinds.
The Demons' only serious forward foray for the quarter ended with a wide behind after Jamie Bennell mistimed a kick to Watts, who failed to mark despite a hard running effort.
While Bailey labelled the Demons' performance their worst for the season, the result had Worsfold rethinking a 2010 finals appearance.
"I would love to play in the finals and hope we can win enough games to play in the finals," he said.
"The challenge is there for us to do that. We've generally played pretty intense footy this year and a couple of games that we've been below what we expect.
"But we haven't had too many easy wins. They're all pretty hard fought for us at the moment but we'll keep fighting for them."
Melbourne 1.3 5.5 6.8 6.10 (46)
West Coast 3.0 5.5 8.8 10.15 (75)
GOALS
Melbourne: Green 2, Bennell, Hughes, McDonald, Scully
West Coast: Kennedy 2, LeCras 2, Lynch, A Selwood, Cox, Ebert, Rosa, McKinley
BEST
Melbourne: McDonald, Grimes, Moloney, McKenzie, Bruce, Green
West Coast: Priddis, Rosa, A. Selwood, Cox, LeCras, Ebert
INJURIES
Melbourne: Bate (left ankle), Davey (concussion), Bruce (hamstring)
West Coast: Nil
Reports: Nil
Umpires: Meredith, Wenn, Mollison
Official crowd: 28, 592 at the MCG
The views in this story are those of the author and not necessarily those of the clubs or the AFL.
