The Demons were jumped by the reigning premiers in Friday night's qualifying final at Ikon Park, conceding the first three goals of the game.
But Melbourne rallied in the second quarter, keeping Adelaide scoreless and kicking three goals of their own to grab the lead by halftime.
Adelaide remained in the hunt at three-quarter-time, trailing by just four points, but the Demons booted the only three goals of the final term to seal a 7.6 (48) to 4.3 (27) victory.
The Demons kept the Crows to just 1.1 after quarter-time and booted seven goals of their own.
Melbourne completely dominated territory after the first 20 minutes when the Crows could not have made a more explosive start.
Classy Adelaide forward Danielle Ponter snapped the first goal after just 15 seconds, before two Caitlin Gould majors truly shocked the highly-fancied Demons.
But Melbourne were able to get on top in the midfield, limiting the true impact of Crows premiership stars Ebony Marinoff and Anne Hatchard.
Olivia Purcell stepped up with one of the best games of her career, having 26 possessions and booting a crucial goal in the second quarter.
Sarah Lampard and Alyssa Bannan were dynamic up forward, booting two goals each to cause havoc for the Crows defenders.
Even Demons ruck Lauren Pearce got in on the action, snapping a brilliant goal from long-range just before halftime.
Adelaide captain Chelsea Randall made a shock return from injury, just two weeks after suffering a badly rolled ankle.
The Crows' premiership hero was clearly not at her best, collecting seven possessions and suffering a big knock late in the contest.
Melbourne, who missed out on securing the minor premiership by 0.3 per cent last week, are now just one win away from a second-straight grand final.
The Demons lost last season's decider to the Crows but appear set to be on a collision course with minor premiers the Brisbane Lions in the decider.
Adelaide will host a semi-final next week against the winner of Sunday's match between Collingwood and the Western Bulldogs.
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