Riccardo Montolivo missed Italy's second penalty but then Ashley Young and Ashley Cole failed to score before Alessandro Diamanti stroked home the winning spot-kick.
It was England's sixth exit in penalty shoot-outs at European Championships and World Cups in the last 22 years.
Roy Hodgson's side had rode their luck to stay on level terms after 120 minutes as Italy were far the better side with 35 attempts on goal, to England's nine, but failed to break the deadlock thanks to their own profligacy and some dogged English defending.
However their greater nerve from 12 yards means it will be the Azzurri who will face Germany in Thursday's second semi-final at the same ground and Hodgson's side go home.
There were chances aplenty in an open first-half.
The tone was set as early as the fourth minute when the ball was pulled back from the right to Daniele De Rossi who hit across his effort from 30 yards and was so unlucky to see the ball hit the woodwork with Joe Hart beaten.
England's best chance of the opening period came almost immediately when James Milner's square pass was poked towards goal by Glen Johnson from seven yards but Gianluigi Buffon clawed the effort away.
Johnson then produced a superb cross but Wayne Rooney could not direct his diving header on target from eight yards, under pressure from covering right-back Ignazio Abate.
That was after 15 minutes but from then on it was Italy who dominated with Andrea Pirlo pulling the strings in midfield and Mario Balotelli spurned a hat-trick of first-half chances.
He beat the offside trap but dallied which allowed John Terry to get back to make a crucial block and he failed to get much power on a scissors kick after a defence splitting pass from Montolivo.
But his best chance came five minutes before the break when Pirlo's cross to the back post was headed across goal by Antonio Cassano and somehow the Manchester City forward stabbed over the top from four yards albeit under pressure from club-mate Joleon Lescott.
Danny Welbeck did spurn a chance to test Buffon from 18 yards after a good link-up with Rooney but Italy continued to be in the ascendancy and were totally dominant in the second.
De Rossi missed a sitter four minutes after the break after Hart punched a corner only as far as Montolivo whose header was volleyed wide from seven yards by the unmarked veteran.
England's goal continued to lead a charmed life as a 30-yard blast from De Rossi was parried by Hart straight into the path of Balotelli who was denied from close range by the legs of his Eastlands team-mate before Montolivo volleyed over under pressure from Johnson.
Theo Walcott and Andy Carroll were brought on after an hour as England struggled to maintain possession and they carved out a rare chance as the Arsenal winger's cross intended for the big Liverpool striker fell to Young whose shot was deflected behind for a corner.
Hart made a sharp shot from Italian sub Diamanti before Johnson made a superb block after Marchisio's superb pass found another sub Antonio Nocerino.
England did have a chance to steal it in injury-time but Rooney's bicycle kick was over the top.
They failed to create a single chance in extra-time as they spent most of the 30 minutes camped in their own half as Italy continued to pile on the pressure.
Hart was grateful to see Diamanti's mis-hit cross strike the outside of the post and the former West Ham man was off target from 10 yards after Federico Balzaretti fizzed a ball across the area.
Italy finally found the net after 115 minutes when Nocerino headed home from close range but he was correctly ruled offside.
Although Italy have won a World Cup final in a shoot-out they had also lost five of their other six encounters and would have feared the worst when, after Balotelli and Gerrard had scored the opening efforts, Montolivo dragged his effort well past the left post.
Rooney smashed his penalty into the left corner before Pirlo had the audacity to produce a 'Panenka' chip down the middle to level at 2-2.
The disappointing Young then smashed his effort against the crossbar before Nocerino calmly placed his shot into the left corner.
Cole's effort was then saved, low to his left by Buffon, and it was left to Upton Park reject Diamanti to condemn England to their eighth quarter-final defeat in nine attempts at major tournaments away from Wembley.
It was eight years to the day since England were knocked out by Portugal on penalties in the quarter-finals of Euro 2004 and Three Lions fans can add Italy to Argentina, Germany (twice) and Portugal (twice) as nations who have held their nerve to beat their side in shoot-outs.