Italy started stronger and took the lead with a well-worked goal from Riccardo Montolivo in the 11th minute, but the world and European champions levelled against the run of play when Xabi Alonso netted from the penalty spot.
Spain looked the more likely to add to the scoreline in the second period until Aquilani's shot deflected off Raul Albiol's foot to leave Victor Valdes wrong-footed six minutes from time.
"We started a little timidly but we have put in a great effort especially in the second half," Spain coach Vicente del Bosque told reporters, after another patchy performance in a friendly match.
"I'm generally pleased when you consider the setbacks we suffered [injuries to Fernando Torres, Gerard Pique and Andoni Iraola]. It was when we were playing at our best that the defeat came."
Italy tore into a weakened Spanish side showing greater urgency and aggression. Domenico Criscito lashed a shot against the post and soon after provided the pass for Montolivo to get behind the visitor's defence and score with a sweet lob.
Iker Casillas had to make good saves from the lively Guiseppe Rossi and Antonio Cassano, who caused the Spanish defence all kinds of problems, but the visitors had a lucky break to equalise.
Fernando Llorente, who had come for a concussed Torres early on, was pushed in the area and Alonso put the scores level in the 36th.
Both sides rang the changes in the second half, one of the most notable substitutes being the debut of Barca's promising 20-year-old midfielder Thiago Alcantara for Spain.
Del Bosque's side dominated with David Silva and David Villa leading Spain forward until Aquilani set up an exciting finish with his fortuitous shot.
"While we had the legs and freshness of thinking we played a good game then we lost a bit of order and we had to work harder," Italy coach Cesare Prandelli told reporters. "But we showed personality and courage."
