BGT judges Alesha Dixon and Amanda Holden were present at the ceremony but it was Claudia Winkleman and Tess Daly who went up on stage after their show won.
Strictly and BGT went up against the TFI Friday Anniversary Special on Channel 4 and Adele at The BBC for for Best Entertainment Programme.
Claudia joked: "I really am regretting the three tequilas," as she vowed to party for days.
She added: "Huge thanks to the producers, the judges and our amazing dancers, we cannot believe it. We're going out for five days after this."
Tess said she was "genuinely shocked" as the pair received the award on the show's behalf.
She said: "This is the most incredible honour, we have never won a BAFTA before and it honestly means the world to all of us, so thank you to everybody at BAFTA."
Also there was Strictly judge Craig Revel Horwood.
"I could not believe it, when Strictly was called out I had to look around twice," he confessed. "I think what stands us above the rest is my judging! But no the show is brilliant.
"The fact that it is a live show and it's going out live. I'm really proud to be a part of the show."
Strictly will be back for a new series later this year on BBC One.