The giant goalkeeper saved from Jadon Sancho and, decisively, Bukayo Saka after Marcus Rashford hit the post, as Federico Bernardeschi, Leonardo Bonucci and Domenico Berardi all scored for the Italians in the shootout.
Luke Shaw had given England a dream start with a superb goal after two minutes but Italy, which offered almost nothing in response in the first half, gradually took command and deservedly levelled through Bonucci after 67min.
For England coach Gareth Southgate, who missed from the spot when his side lost in the Euro96 semifinal to Germany, it was another shootout horror show.
The two players he sent on late in extra time with penalties in mind missed their attempts, as did 19-year-old Saka, who crumpled under the pressure of taking the final kick.
Italy has now won five and lost six of its 10 major tournament shootouts, including one win and one loss in World Cup finals, while England’s dismal record now reads seven losses from nine.
But England fans dreaming of a second title to add to the 1966 World Cup can hardly complain they were robbed this time, after their team followed a strong start by surrendering the initiative despite the support from most of the 67,000 crowd.
The match statistics told the story as Italy had 66% possession and 19 shots to England's six and, until the shootout, Donnarumma barely touched the ball.
Italy is now unbeaten in 34 matches, underlining the stunning turnaround fashioned by coach Roberto Mancini who took over after the country’s humiliating failure to qualify for the 2018 World Cup.
"It was impossible even to think about this, but the guys were extraordinary," Mancini said.
"We were great. We conceded an early goal and had some problems but then we dominated."
It had all started so well for England when Harry Kane spread the ball wide to Kieran Trippier and he instantly repaid coach Southgate’s faith in recalling him by sending over a curling deep cross that Shaw met on the half volley to hammer inside the post for his first international goal.
England had taken an early lead in its 2018 World Cup semifinal against Croatia before being outplayed and losing in extra time but for a while it stayed on top, with the Italians arguing and running to Mancini for instructions as they struggled for a foothold.
England’s well-drilled defence, which had conceded one goal, via a Denmark free kick, in its six previous tournament games, looked safe enough but the players in front gradually began to concede more and more territory.
Jordan Pickford had to save from Lorenzo Insigne and Federico Chiesa as Italy cranked up the pressure and it paid dividends when Bonucci pounced from close range after the keeper had turned Andrea Belotti’s header on to a post.
England could have no complaints after inviting its opponent on and offering almost nothing in attack.
England briefly sensed glory in the shootout when Pickford saved from Belotti, and Kane and Harry Maguire put it 2-1 ahead. The keeper kept the host in it again when he saved from Jorginho, only for Donnarumma to have the final word when he blocked Saka’s weakly-struck shot.
"The penalty takers are my call," Southgate said.
"We know they were the best takers we had left on the pitch, and we tried to get those players on to the pitch.
"The players have given everything, not only tonight but throughout the whole tournament.
"They should hold their heads high . . . but the devastation of getting so close is difficult to put into context.
"At the moment the pain of the defeat is huge.
"We wanted to give our nation one more special night and a first European championship and we haven’t quite been able to do it."
