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."
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'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.
