Villa's initial 10-game stay in Melbourne was cut short so the Spaniard could undertake media obligations with his parent club, New York City.
Though Spain's record goalscorer may yet return for another Melboune appearance, he bowed out for now having failed to inspire City to victory in his four appearances.
Damien Duff went close early on at AAMI Park as his volley from Villa's cross was spilled onto the post by Adelaide goalkeeper Eugene Galekovic, but the Irishman kept his chin up to assist Melbourne's opener.
Duff's inswinging corner from the right was flicked home by home captain Patrick Kisnorbo - the defender's first goal since February.
Adelaide roared back though and put plenty of pressure on the Melbourne defence before right-winger Tarek Elrich delivered a peach of a cross which Bruce Djite neatly guided over Andrew Redmayne and into the net.
As the visitors continued to apply pressure in the second half, Kisnorbo was perhaps lucky just to see a yellow card after felling Djite as the striker burst clear on goal.
But Adelaide grabbed a deserved winner 12 minutes from time, Bruce Kamau dribbling into the area before being brought down by Redmayne, allowing Marcelo Carrusca to net the penalty.
Three points put Adelaide top of the league with 10 points from their first four games, but Melbourne's struggles continue despite their high-profile pre-season signings.
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