Turning themselves into a giant robot, they had judges and the audience on their feet cheering wildly as they moved in time with a series of dazzling leaps, somersaults and breakdance moves.
They will now appear in front of the Queen at the Royal Variety Performance later this year.
Susan chose the same song from Les Miserables as she sang during her original audition.
She wore a sparkling, floor-length gown and won a standing ovation from the studio audience.
Simon Cowell told her: "Win or lose, you had the guts to come back here tonight, face your critics and you beat them."
Boyle now stands to make an estimated £8million fortune from a glittering singing career, having been plucked from obscurity just a few weeks ago.
The other act to make the final three was Julian Smith.
Prior to the show going out, it was revealed Susan has already been approached to appear in an episode of the hit American TV series Ugly Betty - broadcast on Channel 4 in the UK.
An insider said: "She had a good laugh when she heard - she was the first one to spoke the joke.
"But of course she would love to do it after the final.
"It's a brilliant way of boosting her profile even further in America.
"It's a small walk-on role - and she will be playing herself.
"Susan joked: 'I might not be a stunner but I'm better looking than Betty!'"
On Saturday, Talent judge Piers Morgan had called on Boyle's critics to stop sniping.
Pressure
Speaking on Sky News at lunchtime, Piers played down public fears about Boyle's well-being following reports that was feeling the pressure as the big night approached.
He said: "Susan Boyle is a very, very nice lady from Scotland who never thought she would have this chance."
Piers, who judges alongside Simon Cowell and Amanda Holden said it "angered" him that people were "trying to get inside her head" amid speculation over the effect that the stress of the competition is taking.
Boyle denied a foul-mouthed outburst while watching Britain's Got Talent on television at her hotel earlier this week, he said, and responded angrily to two journalists because she is "feisty".
"Susan is a feisty lady, she is not a little kitten, she is a very feisty lady from Scotland who has had a tough life and she wasn't going to take any nonsense and I applaud her for that."