The Crows delivered a stunning run of six consecutive goals across the second and third quarters, then withstood a late Melbourne charge for an 8.8 (56) to 7.4 (46) win at Casey Fields.
The result ended Melbourne's 14-game winning run stretching back to last season.
Superstar midfielder Ebony Marinoff led the charge for Adelaide, booting two goals from 27 disposals and laying 13 tackles, alongside Anne Hatchard (32 touches and two goals) and Danielle Ponter (two goals).
"That was just an incredible contest," Hatchard told Fox Footy.
"We knew the Demons would come out fighting and our group just came together and played a magnificent game of footy.
"It's definitely a confidence booster.
"We definitely came in (as) the underdogs and to be able to come out and play that footy's just awesome."
The brilliant Eden Zanker booted five goals for Melbourne, almost hauling the Demons over the line.
With Paxy Paxman (concussion) sidelined, Tyla Hanks (22 touches, 12 clearances), Kate Hore (19 touches, six clearances) and Olivia Purcell got to work in midfield.
Eden Zanker (right) kicked the first two goals of the game for Melbourne against Adelaide.
Zanker booted the first two goals of the game as Melbourne earned a 16-point quarter-time lead, with Adelaide scoreless.
Then, the Crows took off.
Ponter and Marinoff helped their side draw level at halftime as Adelaide held the Demons to their first scoreless quarter of the season.
In the third term, Melbourne had no answers for Adelaide's fierce intensity and pressure.
Hatchard went forward and put the Crows in front for the first time, before Marinoff, Eloise Jones and Ponter extended the lead to 25 - a 41-point turnaround.
Eliza McNamara scored a goal seconds before three-quarter time to cut Adelaide's lead to 19.
Zanker took back-to-back huge contested marks and kicked truly both times to cut the deficit to seven points early in the final term.
But when Tayla Harris bumped Marinoff late as she kicked inside 50, Hatchard earned a downfield free kick and coolly converted to give the Crows some breathing room.
Melbourne hadn't conceded a fourth-quarter goal in their previous 14 games.
McNamara and Zanker each struck again as the Demons made a late charge.
But Caitlin Gould ran into an open goal to seal victory for Adelaide.
