Howard saved United's first two spot-kicks from Dimitar Berbatov and Rio Ferdinand after a turgid semi-final ended 0-0 after extra time at Wembley Stadium.
Everton will return to Wembley for the final on May 30 against Chelsea, who beat Arsenal 2-1 in Saturday's first semi-final.
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Everton defender Phil Jagielka scored the winning penalty, blasting the ball past goalkeeper Ben Foster to inflict United's first defeat in an FA Cup semi-final since 1970.
United manager Alex Ferguson gambled by playing a largely reserve side and defeat ended the European champions' hopes of winning an unprecedented five major trophies this season.
"It was a tough game for us. Man United, whoever they play, they could put out their under-14's and it would have been a tough game because they play to win every competition that they are in," Everton manager David Moyes said in a televised interview.
"I thought we kept at it, I thought we could have played better at times but Man United made it difficult for us."
POOR MATCH
The match itself was largely devoid of inspiration with neither team gaining control and play largely meandering around the midfield.
Everton had half a chance when Foster dallied too long on a loose ball and almost lost it to former United striker Louis Saha whose attempt at goal slammed into the goalkeeper's chest.
United threatened after 23 minutes when Everton defender Joleon Lescott deflected a shot just wide of his own goal.
United's unfamiliar line-up largely spluttered on the stodgy Wembley pitch and twice good moves down the right ended in disappointment when young striker Danny Welbeck failed to deliver a decent cross.
It was not until the 54th minute when Everton midfielder Tim Cahill had a shot on target that either goalkeeper was forced into a genuine save, and even then Foster was hardly troubled by the Australian's long-range shot.
Carlos Tevez and Park ji-Sung never stopped working for United in midfield but Federico Macheda, the 17-year-old Italian who has scored two vital late goals as A substitute in recent league matches, was virtually anonymous on his full debut.
United appealed furiously for a penalty after 68 minutes when Welbeck appeared to be clattered by defender Jagielka and Ferguson was enraged when referee Mike Riley ruled there had been no infringement.
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