Three rapid-fire chances in the 52nd saw Hart beat away De Rossi's long-range shot, block Balotelli's follow-up and watch Montolivo lash the loose ball high.
England coach Roy Hodgson had to react to Italy's dominance, and sent on substitutes Andy Carroll and Theo Walcott, who both scored in a 3-2 win over Sweden.
Carroll's muscular presence created a shooting chance for Young, but England still failed to convince. Rooney made little impression after an early diving header.
De Rossi was replaced by Nocerino and the substitute threatened in the 89th. He took another crafty pass from Pirlo on the run, but Johnson tracked back to block.
Deep into injury time, Italian defensive jitters created a chance for Rooney but his overhead kick sailed high.
Then it was on to penalties. And Diamante's heroics.
"Getting to this point is a huge satisfaction," Diamanti said. "I always believed I would, even when I played in the inter-regional division — I just never told anyone, because they would have thought I was crazy."
Italy wins 4-2 on penalty kicks
Euro 2012 semifinals
At Donetsk, Ukraine
Portugal vs. Spain, 12:45 p.m.
At Warsaw, Poland
Germany vs. Italy, 12:45 p.m.
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