The London trio were amazed to get four yes votes from the BGT panel after they performed I Got the Music in Me by KiKi Dee.
Renetta, 18, Ebony,15, and Alexis, 21, stood in shock as Alesha told them: "You look adorable together...and I definitely, definitely think you deserve a chance."
"I think we've found something special in you," added Amanda Holden.
Simon Cowell was also on board with the girls' potential to do well on the show, but he warned them: "(Your) vocals need a lot of work, but I think you've naturally got good voices."
The positive feedback from the judges was enough to reduce the girls to tears, but they were even more shocked when Alesha hit the golden buzzer in response to whether or not they should go through to the next round.
This now means the girls will proceed straight through to the live semi-finals.
Speaking about her decision, Alesha said: "I started out in a girl group and I wouldn't be here if it wasn't for Mis-Teeq so that's what I saw in those girls and that's why I want to support you the whole way."
I love the chemistry, I love your relationship. I think we've found something special in you.
Amanda Holden to REAformed
Before the excited group left the stage, Simon told them they would now have to "live up to Alesha's potential" in their next performance.
Meanwhile it was also an emotional audition for 40-year-old supermarket worker Eva Iglesias, who, after being rejected by other television shows including The X Factor, felt this was her last chance at success.
Eva impressed the judges with a passionate vocal performance of Aretha Franklin's Natural Woman and earned four yes votes from the panel.
David Walliams said: "We never have anyone, hardly ever who comes on and sings with that passion and emotion. You really were singing from the heart, it was like your life depended on it."
Eva told the judges she nearly didn't turn up for her audition as she had very recently had her heart broken.
"They just didn't want to love me anymore," she said.
Simon told her: "You came out here and that is one of the most beautiful songs of all time, written by Carole King, and her heart was broken when she wrote that song. I understand why you were giving it what you gave it."
There's this guy backstage that everyone is talking about. His name is Anton... Anton Dec? I think he's French.
First to audition during Saturday's show was the delightful and mischievous Patsy May, who not only won the hearts of the audience, but Ant and Dec were also wooed by the mini diva.
She invited the Geordie pair to join her on stage, and serenaded them with a little bit of Dream A Little Dream Of Me, earning herself a kiss from both the boys.
Also smitten with Patsy was Simon, who told her: "I kind of see you in Amanda's chair next year."
Amanda did not seem amused...
Swing boyband Jack Pack had the audience and the judges on their feet following their rendition of That's Life by Frank Sinatra, with Alesha describing them as "perfection".
Essex teen Kieran Lai also received a positive reaction after he performed a popping and locking dance routine inspired by The Tin Man from The Wizard of Oz.
Amanda said: "It's like you're made of plasticine. The shapes you made with your body was like you weren't human!"
And Irish duo Terri & Lisette left the panel amazed after their pole dance acrobatic performance, with David describing them as "the Ant and Dec of pole dancing".
Britain's Got Talent returns to UTV next Saturday at 7.15pm.