Beau, Amanda Holden's Golden Buzzer act, came top of public vote - with Balance and Tumar KR facing the judges as the second and third-placed hopefuls.
Unusually, the panel delivered a unanimous decision, with Balance going straight through after David Walliams, Alesha Dixon and Amanda all sided with him.
When presenter Dec asked Simon Cowell what his decision would have been, he responded: "You were amazing Balance, you've got four yesses."
The full leaderboard for the fourth live show was:
Britain's Got Talent 2016 fourth semi-final results
1. Beau Dermott (won public vote)
2. Balance Unity (won judges' vote)
3. Tumar KR (lost judges' vote)
4. Vox Fortura
5. The Collaborative Orchestra and Singers
6. Christian Lee
7. Danny Beard
8. Bollywest Fusion
9. Bespoke Candi
Bollywest Fusion opened with another fantastic Bollywood-hip hop dance routine David described as a "feast for the eyes".
The Collaborative Orchestra took over the whole studio for another rousing performance. "This act has got the Royal Variety Show written all over it," said Amanda.
Dinosaur dancers Bespoke Candi caused a kerfuffle among the judges, with Alesha hitting THREE of their buzzers - before Vox Fortura united them in praise, with David remarking that if he was Simon he'd "make you sign a record contract right now".
Balance received mixed reviews, with Simon noting that he didn't need backup dancers - but it was Danny Beard that received the mogul's most scathing review.
"I thought it was pointless," he told the drag act. "I think you missed a fantastic opportunity to do something different, this was just cabaret."
Comedy magician Christian enlisted David as his assistant for his latest trick, before Tumar KR's robotic dance routine had the panel on their feet. "I actually think if we cut you open wires would come out! It was horrific, but brilliant!" gasped Amanda.
Beau also won a standing ovation. "It wasn’t the fact you’re 12 years old, you’ve just got a good voice," Simon reviewed. "I guarantee in five years we’ll look back and think, 'this is the moment we discovered a star'."
Beau and Balance join Richard Jones, Boogie Storm, Wayne Woodward, Alex Magala, 100 Voices of Gospel and Mel and Jamie in the line-up for the final, which takes place on Saturday.
This year's last Britain's Got Talent semi-final airs tomorrow at 7.30pm on ITV, featuring Ant and Dec's Golden Buzzer act Jasmine Elcock.