The Northern Ireland-born rider joined trainer Gary Moore earlier this year, having previously been based with Warren Greatrex, and was given an opportunity on the big stage in this £125,000 contest.
Botox Has, winner of the Grade Two National Spirit Hurdle in February, was a 17-2 chance off the back of finishing second on his seasonal reappearance at Cheltenham last month.
Always close to the fore, the six-year-old found plenty for pressure after the final flight to score by two and a quarter lengths from Get A Tonic, with Cesarewitch hero Run For Oscar best of the rest in third.
Quinn, aged 21, said: "I'm speechless to be honest. He's a tough horse, I just tried to keep on the bridle and luckily enough I was in the right place the whole way.
"When they've come to him, he's winged the last and really put his head down and battled for me.
"He's very brave - the more you ask him the more he gives you. He's a wonderful horse.
"He's still unexposed and there's still plenty of improvement in him I think, so the future is exciting for him.
"I can't thank Mr Moore enough. Since I've moved there he's trusted me with some very good rides and hopefully I can keep delivering for him."
The Moore team were also on the target at Ascot, with the popular Goshen landing the Coral Hurdle.