Antonio Di Natale put the Azzurri ahead in the second-half, latching on to an inch-perfect Andrea Pirlo through-ball and slotting it with his right foot past the advancing Iker Casillas.
But Cesc Fabregas equalised within minutes at the other end after David Silva split two Italy defenders with a neat pass, leaving Gianluigi Buffon helpless.
Barcelona star Andres Iniesta described the draw as "bitter-sweet", while Italy coach Cesare Prandelli said his team had allowed Spain back into the game.
"We've given Spain the opportunity to equalise, so we have to improve and that's the mentality we need," he added.
Spain's shaky start was in contrast to Germany, whom they beat in the final four years ago and who are out for revenge this time round. They at least managed to get three points in a laboured 1-0 win over Portugal on Saturday.
The Italy team will take heart from the match after a torrid build-up, when police raided their pre-tournament training camp as part of a nationwide probe into illegal betting on football.
The team later had to cancel a warm-up match against Luxembourg after an earthquake rocked northern Italy and were then thumped 4-0 by Russia in a friendly.
In the second Group C match, Croatia beat Republic of Ireland 3-1 in the western city of Poznan, thanks to a brace from Mario Mandzukic.
Mandzukic opened the scoring within minutes, beating Shay Given to his left from 12 yards out with a header before Sean St Ledger levelled the scores.
But Nikica Jelavic put the Croats back in front just before half-time. Mandzukic then saw another header go in after the break, with the ball bouncing back off the left-hand upright and hitting the luckless Given's head as he dived.
Croatia looked likely to face sanctions, though, after their fans lit flares and let off smoke bombs to celebrate the first-half goals.
Germany is facing disciplinary proceedings after missiles were thrown in Lviv and Portugal are being investigated after the second-half kick-off was delayed.
UEFA has already initiated proceedings against Russia after its fans lit and threw fireworks and displayed potentially inflammatory "Russian Empire" flags at Friday's Group A game with the Czech Republic in Wroclaw, Poland.
It also said it was investigating claims from a racism monitoring body that the Czech's Theo Gebre Selassie, who is black, was subjected to monkey chants during the game, which Russia won 4-1.
Police are separately probing an attack on four volunteer stadium stewards after the match, and are publishing photographs of six Russian suspects.
Russian football chiefs have vowed to do all they can to prevent a repeat of the violence.
But the country's football supporters association accused the Polish stewards, who required hospital treatment afterwards, of provoking the attack by trying to detain what they said was an innocent fan.
Wroclaw police said meanwhile that two Russia fans were each given two-year bans from Polish football grounds and a 2,000-zloty (460-euro, $575) fine for ignoring requests by security personnel during the match.
Four other Russia fans were charged in connection with a restaurant brawl while 10 Poles, four Irish and one Croat were held after violence in Poznan.