Adelaide went ahead before even two minutes had been played, through a combination of poor defending and a healthy dose of luck.
Pablo Sanchez whipped a cross in to the back post, and Sebastian Ryall's attempted clearance cannoned off Cirio and into the back of the net past a stunned Vedran Janjetovic.
It was a huge piece of fortune.
A helter skelter final ten minutes of the first half saw three goals scored and therefore nothing separating the teams at the interval.
An immaculate diving header from the often-maligned Matt Simon dragged Sydney level after a wonderful cross by Filip Holosko.
Simon drove between Adelaide's centre backs before flicking his header past Eugene Galekovic.
On the cusp of the break, Adelaide put their noses in front again, thanks largely to Bruce Kamau.
The Adelaide winger beat Rhyan Grant too easily, before feeding Cirio, who turned and fired a shot into the bottom corner for his brace.
Graham Arnold will have wondered how Cirio, surrounded by no less than six sky blue shirts, managed to get a shot away.
But just when it looked like the Reds would take the lead into the break, Sydney drew level again.
Milos Ninkovic this time was the architect, arcing a beautiful pass to Holosko, who after an attempted clearance by Jordan Elsey, dinked the ball past Galekovic to make it 2-2.
It was breathless stuff and the break was a welcome one.
Sydney came out with renewed intent in the second half, and Chris Naumoff should have done better with a back post volley early in the second period.
Marcelo Carrusca came on around the hour mark as Adelaide looked to inject some creative spark, while Simon lashed a half-volley over the crossbar from the edge of the area.
Stefan Mauk had a wonderful chance to put Adelaide ahead but he fluffed his lines in front of goal, before Sydney began to pile the pressure on.
One would wonder why Arnold waited until the 82nd minute to inject the A-League's second-top goalscorer of all time, Shane Smeltz, into the contest, but a draw proved a fair result.
Adelaide United 2 (Cirio 2', 45')
Sydney FC 2 (Simon 37', Holosko 45+3')
Coopers Stadium, Adelaide
Referee: Chris Beath
