In a clash between two fierce traditional rivals, the away side took the lead twice through Cirio, but gave it up on each occasion to an inspired Guilherme Finkler.
Victory opened up a two-goal lead through strikes from Archie Thompson and Kosta Barbarouses, before Cirio netted his hat-trick with seven minutes to go, making it a nervy finish for the home side.
But the hosts managed to hold out, the win seeing them climb above Adelaide and Sydney and into third on the table, reviving their hopes of top-two finish.
There will be more headaches for Victory coach Kevin Muscat in the days ahead however, with a yellow card ruling Pablo Contreras out of the derby against Melbourne Heart at the same venue next Saturday night.
Perhaps more seriously, and with potential repercussions for both club and country, Socceroo Tom Rogic limped off due what appeared to be a foot or ankle problem following an accidental collision with team-mate Leigh Broxham early in the second half.
Depending on the extent of the injury, Rogic may be forced to sit out the Asian Champions League group stage opener away to Guangzhou Evergrande on Wednesday night.
With that game in mind, Finkler, not selected in the ACL squad, replaced Barbarouses in Victory's starting XI, while Tarek Elrich came into the Adelaide line-up for the suspended Michael Zullo.
The hosts barely had a chance to settle before finding themselves a goal down three minutes in. Isaias' carefully weighted ball released Fabio Ferreira in behind Adama Traore, and although the winger's cutback evaded Bruce Djite, Cirio got free of Scott Galloway at the back post to tuck the ball home.
Adelaide's insistence on playing out from the back saw them caught out after 15 minutes. Broxham harried Nigel Boogard into giving the ball straight to Thompson, who picked out Finkler with something of a heavy pass. The Brazilian, played just onside by Boogard, took a touch which saw the ball loop up high in the air.
Undeterred, he watched it back onto his foot and hit a well-placed shot beyond Eugene Galekovic and into the far side-netting.
An increasingly spiteful game saw challenges flying in on both sides, but also produced chances. Ferreira for Adelaide and James Troisi for Victory both went close to scoring, before the visitors regained their lead in the 45th minute.
Djite did well to steal possession and then hold off Nick Ansell, before tucking a pass between the centre-back's legs to play in Cirio. The Spaniard, again breaking free of Galloway, then dinked a delicate finish over the on-rushing Nathan Coe to make it 2-1.
In the 56th minute, Victory were level and had Broxham to thank. Finkler managed to keep the ball in on the byline and played it back to the midfielder, who showed quick feet to beat two Adelaide defenders. Broxham returned possession to Finkler and the on-song forward did the rest, squeezing a shot past Galekovic at the keeper's near post.
The hosts took the lead for the first time in the game 10 minutes later, and did so courtesy of a gift from Galekovic. Troisi played a ball over the top of the defence for Thompson to chase and while the usually reliable Adelaide custodian rushed out of his box to clear, he got the execution all wrong.
With Galekovic stranded in no-man's land, Thompson was able to collect the loose ball and finish from a tight angle into the empty net.
Both teams could have had penalties within the space of 60 seconds mid-way through the second half. At one end Coe appeared to trip substitute Jeronimo Neumann just inside the penalty area, before Thompson was felled in Adelaide's area, only for referee Kris Griffiths-Jones to wave away any appeals.
Neither side had time to process their disappointment before Victory struck again. A quick, accurate clearance found Barbarouses one-on-one with Jonathan McKain and the new arrival toyed with his man long enough to find Finkler, who demonstrated great skill to carry the ball into the Adelaide box and shoot at Galekovic.
Troisi collected the rebound and squeezed past the goalkeeper right on the byline, before delivering across the face of an empty goal. Fittingly, Barbarouses was on hand at the back post to complete the brilliant move and make it 4-2.
With nine minutes to go Adelaide saw yet another legitimate penalty claim ignored when the ball struck the hand of Contereras, it didn't matter though, as Cirio reacted quickest to smash the ball home and complete his hat-trick.
A late Reds onslaught included Galekovic going forward for a free-kick in search of redemption, but they were unable to force an equaliser, and the final whistle prompted deafening cheers from the home supporters.
Melbourne Victory 4 (Finkler 15', 56', Thompson 66', Barbarouses 75')
Adelaide United 3 (Cirio 3', 45', 83')
Crowd: 18,341 @ AAMI Park
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