Substitute Di Natale edged Italy ahead on the hour mark but Barcelona midfielder Fàbregas finished from close range moments later to rescue a point for Vicente Del Bosque’s men.
Spain, the heavy favourites ahead of the tournament, were less-than-convincing against a well-organised Italy outfit, who were able to frustrate the world champions while holding their own in the final third.
David Silva missed the first opening for Spain in the 10th minute when the Manchester City midfielder raced through on goal but his tame effort was easy for Gianluigi Buffon.
Andrea Pirlo then kept Iker Casillas on his toes when the veteran midfielder struck a curling, low free-kick which the Real Madrid goalkeeper was forced to push wide.
Del Bosque raised a few eyebrows by fielding a side without a recognised striker, opting to leave the likes of Fernando Torres and Fernando Llorente on the bench.
But Spain, who had only triumphed once in a competitive fixture against Italy ahead of Sunday’s clash – the Euro 2008 quarter-final – were dominating the possession stakes in Gdansk.
Yet it was Italy who were creating the better goal scoring chances, with Claudio Marchisio testing Casillas from range with a stunning volley from Antonio Cassano’s cross in the 36th minute.
Spain continued to play their way into dangerous situations but seemed unable to carve out clear-cut opportunities as an Italy rearguard marshalled by Giorgio Chiellini held firm.
As the half went on, Andrés Iniesta, who had already embarked on a couple of brilliant and seemingly effortless mazy runs through Italy’s back four, had a superb chance to put his side ahead when he collected Xavi’s pass – but his dipping effort landed on the roof of the net.
The best chance of the half fell to Thiago Motta at the other end on the stroke of half-time, when his header from Cassano’s cross forced a brilliant save from Casillas from point-blank range.
Fábregas signalled his intent four minutes into the second half when the Barcelona midfielder forced a good stop from Buffon with a curling effort.
Iniesta then saw his shot fly just wide from an acute angle as Spain continued their bright start to the second period.
Mario Balotelli had a brilliant opportunity to edge his country into the lead when he won possession off Sergio Ramos – but the Manchester City striker dithered on the ball too long, allowing the Real Madrid defender to make amends with a last-ditch challenge as the chance went begging.
Balotelli was almost immediately replaced by Di Natale, whose impact was instant.
Slid through on goal by Pirlo’s perfectly-weighted pass, Di Natale maintained his cool to slot his effort to the right of Casillas in the 60th minute.
But Italy’s advantage was short-lived.
As Spain poured forward, Silva dinked a pass through for Fábregas, who swept the ball home from close range to equalise for the holders. Italy’s lead had lasted less than 90 seconds.
Substitute Torres, on for Fábregas, had a great chance to fire Spain into the lead when he appeared to be through on goal – but his attempt to take the ball around Buffon was foiled by the Italy shot-stopper, who managed to gain possession and clear.
Torres and Marchisio both had chances to win it as the game opened up towards its conclusion but there was to be no winner.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news