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Italy pulled one back with nine minutes to go after a quick one-two by Vincenzo Iaquinta and Fabio Quagliarella. When Jan Mucha parried out a sure goal, Di Natale was on hand to hit the ball in.
Then a throw-in by Peter Pekarik caught Italy off guard and Kamil Kopunek were quick enough to lob the ball over Italian keeper Federico Marchetti.
Quagliarella cut Slovakia's advantage with a cannon shot two minutes into the stoppage time but Simone Pepe wasted their last chance when he struck wide at the far post.
Italy coach Marcello Lippi took all the blame by himself.
"I assume complete responsibility for this failure," he said. "I was convinced this squad could do a lot better than that - not win the World Cup, but do a lot better.
"When a team goes into a match as important as this with fear in the stomachs and paralysis in their legs, it's because the coach hasn't prepared them well enough mentally, physically and tactically, but above all mentally."
The gray-hair guru coach was emotional in the post-game press conference.
"I offer my apologies to Italian sport, the players, the football association - everyone," he said. "I'm very sad that my adventure with the Italian football association has come to an end in this fashion.