Fernando Torres fluffed two late chances as Spain's hopes of making a winning start to the tournament foundered in Gdansk.
Torres, who has endured a wretched period at Chelsea since joining from Liverpool in January 2011, was sent on by Vicente Del Bosque shortly after Fabregas cancelled out Di Natale's opener.
But he could not conjure up a winner as the opening match in Group C ended all square.
Del Bosque opted to utilise the 'false number nine' formation which saw them line-up without a recognised striker and although there were moments of promise from offensive midfielders Fabregas, Andres Iniesta and David Silva, Spain lacked a focal point until Torres' introduction after 74 minutes.
Silva fired a ninth-minute drive over the bar from 25 yards and the Manchester City man drew an 11th-minute save from Italy goalkeeper Gianluigi Buffon after a swift break from Iniesta.
But the Azzurri's impressive trio of central defenders, Daniele De Rossi, Leonardo Bonucci and Giorgio Chiellini, managed to snuff out the rest of Spain's forays forward in a cagey opening period.
At the other end, Italy, inspired by the impressive Antonio Cassano, offered a genuine goal threat.
Andrea Pirlo saw a free-kick saved by Iker Casillas, who then denied Cassano and Claudio Marchisio, whose blistering volley would surely have gone in had it not been straight at the Real Madrid goalkeeper.
First-half injury-time saw both sides create their best chances of the period.
First, a typically incisive through-ball from Xavi presented a wonderful opportunity for Barcelona team-mate Iniesta but his first touch was uncharacteristically poor, meaning his second only resulted in a tame volleyed lob over the bar.
And then, Cassano escaped down the right and whipped in a wonderful cross for Thiago Motta, whose header was superbly palmed to safety by Casillas.
The Spanish came out with greater verve after the break and Buffon twice had to make smart saves, the first from Fabregas and the second a stunner to deny Iniesta.
But Italy were still causing headaches for Del Bosque's men in defence.
And it led to a momentary lapse in concentration from Sergio Ramos, the Real Madrid central defender dispossessed by Mario Balotelli as he attempted a back pass to Casillas.
Balotelli was clear on goal but took an age to get a shot in, allowing Ramos to get back and smuggle the ball behind for a corner.
It proved Balotelli's final act as he was hauled off by Italy boss Cesare Prandelli in favour of Di Natale.
And the Udinese veteran made an immediate impact as he opened the scoring within four minutes, latching on to Pirlo's inch-perfect pass before coolly slotting past the onrushing Casillas.
A shock seemed on the cards but world and European champions Spain hit back almost immediately.
A beautiful flicked pass with the outside of his left boot from Silva picked out Fabregas and he made no mistake with a crisp finish under Buffon.
Del Bosque finally introduced a striker in Torres and although the former Atletico Madrid man looked sharp, he still appeared short on confidence in front of goal.
After 75 minutes he tried to round Buffon but the Juventus goalkeeper made a clean tackle and, then 10 minutes later, a clever one-two with Xavi saw Torres burst through but his attempted chip drifted narrowly over.
In between, Sebastian Giovinco picked out Di Natale five yards from goal but his volley at full stretch went wide.