Still stung by their second half capitulation against Newcastle Jets last week, Melbourne City came out all guns blazing, and they fully deserved their win.
Erik Paartalu, back in from the cold, Aaron Mooy and Bruno Fornaroli, twice, all scored as John van't Schip's side showed what they are capable of.
Adelaide will be worried however; they are now winless in five. How long Guillermo Amor can survive at this rate is anyone's guess.
If it's any consolation, Cirio's goal broke a 442 minute scoring drought for a Reds' player, strectching back to Craig Goodwin's second half goal against Sydney FC in the semi final last season. Pablo Sanchez's late penalty added a degree of respectability to the scoreline.
Adelaide's previous two goals this season were own goals.
Adelaide were lively but they couldn't quite string it together in the final third, and despite 61 per cent of first half possession, it was City who headed to the sheds with a two-goal lead.
Early on, Marcelo Carrusa's delightful pass released Bruce Djite, who was stopped in his tracks by Thomas Sorensen, who was quickly off his line despite his advancing years.
The Danish keeper made a number of important saves throughout the night.
It didn't take long for a setback to strike the Reds however.
Mooy's corner was swung in wickedly at the near post, and Paartalu headed past the stranded John Hall.
Mooy, fully recovered from his disappearing act in the second half meltdown against Newcastle Jets last week, looked in the mood, and he was spraying the ball around for fun.
Paartalu nearly went from hero to villain when he turned the ball over to Jimmy Jeggo in midfield, but Sorensen made a sprawling save to push the ball wide.
Craig Goodwin and Carrusca were looking the most likely to break open the City defence, but just as the Reds were thinking of an equaliser, Mooy struck to double the visitors' lead.
Ben Garrucio's pass was cleverly dummied by Fornaroli, and when Osama Malik dived in to no avail, Mooy was left in possession on the edge of the area.
His finish was indicative of the confidence with which he is playing, as he lashed it in off the crossbar. Hall, who had gone to ground anticipating a more subtle finish, was left floundering.
Carrusca had a free kick on target which was well saved by Sorensen, and when the ball came back to Goodwin, he shot wide when he probably should have scored.
Djite looked like he'd pulled one back at the stat of the second half but Sorensen spread himself well to block the path to goal.
Fornaroli had looked lively all night and it was no surprise when "El Tuna" wrapped up the game.
He made Malik look silly inside the area, and he showed his class with a lovely clip over Hall. It was Fornaroli's fourth goal of the season, and there will be many more on this evidence.
City, perhaps with the memory of last weekend still lingering, went back into their shell and when Cirio found the bottom corner with a superb curling effort, Adelaide rallied.
But when substitute Harry Novillo sliced open the defence with a razor sharp through ball, Fornaroli rounded Hall to finish the job.
Pablo Sanchez made no mistake with a late spot-kick but Adelaide's race had long been run by then.
Adelaide United 2 (Cirio 66', Pablo Sanchez 86')
Melbourne City 4 (Paartalu 8', Mooy 35', Fornaroli 56', 71')
Melbourne City 4 (Paartalu 8', Mooy 35', Fornaroli 56', 71')
Coopers Stadium, Adelaide
Referee: Kris Griffiths-Jones
