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.
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.
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.
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.
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.
Melbourne Victory 4 (Finkler 15', 56', Thompson 66', Barbarouses 75')
Adelaide United 3 (Cirio 3', 45', 83')
