The visitors had already guaranteed their spot at Brazil 2014 prior to kickoff, and Southampton striker Daniel Osvaldo put them on course for their seventh win of the campaign on 28 minutes.
Nicklas Bendtner scored either side of half time as Denmark came from behind to put themselves on course to leapfrog Bulgaria, who lost 2-1 to Armenia earlier tonight, into second place, only for Aquilani to deny them victory in stoppage time.
Osvaldo opened the scoring by putting the finishing touches to a classy Italian counter attack, controlling a lofted ball over the top from Thiago Motta before finding the top corner with a measured strike.
Their equaliser seemed to give the hosts confidence and they twice struck the woodwork in the space of 12 second-half minutes, firstly through Tottenham Hotspur playmaker Christian Eriksen's 20-yard set piece.
Andreas Bjelland was next to be denied when his drive through a congested penalty area hit the crossbar, but Bendtner enjoyed better luck when his glancing header finished inside of the post on 79 minutes.
The Dane's brace on his first international appearance in six months would only be enough for a point, though, as Aquilani turned home an Osvaldo cross from close range to ensure that Italy remain unbeaten on the road to Brazil.