Lorenzo Insigne, playing his first international for two years, ended Spain's run of six successive clean sheets when he finished off a counter-attack to give the hosts a deserved lead midway through the second half at the Stadio Friuli.
But Aduriz, who made his only previous appearance for Spain six years ago and was recalled thanks to his prolific form with Athletic Bilbao, replied three minutes later from Spain's first shot on target.
The result ended Spain's run of seven successive wins and they would have lost if had it not been for an inspired performance by their goalkeeper David de Gea.
"It's a shame we conceded a goal from a set piece and especially one that was offside, but apart from that it was a good performance," Italy coach Antonio Conte, who announced this month that he would step down after the Euros, told RAI.
"I can assure all Italians that this is a great group of guys and we are a squad who love this shirt," he added.
Italy were missing midfielders Claudio Marchisio and Marco Verratti and defenders Andrea Barzagli and Giorgio Chiellini, while Spain were without forward Diego Costa.
The hosts fielded a 3-4-3 formation and were far livelier than the pedestrian visitors, in particular Antonio Candreva.
The Lazio midfielder produced a wicked cross which defender Sergio Ramos turned against his own post in the sixth minute and nearly scored with a long-range shot which De Gea turned around the post.
De Gea made further saves from Insigne and Alessandro Florenzi before Italy finally went ahead in the 67th minute.
Debutant Federico Bernardeschi set Emanuele Giaccherini free and his low cross was diverted past de Gea by Insigne.
They led for only three minutes before Cesc Fabregas floated a free kick into the area, Gianluigi Buffon failed to hold Alvaro Morata's header and Aduriz fired the rebound into the roof of the net.
Insigne thought he had won the game for Italy with a delightful chip over De Gea but the Spain goalkeeper managed to tip the ball over the bar.
(Writing by Brian Homewood in Berne, editing by Ed Osmond)
