Commissioner Julia McKenzie tweeted a picture of the team picking up the award:
Referencing the Oscars, Cheng tweeted after the event: "It's been a good week for east asians winning awards", adding "chuffed".
Meanwhile in the 'Best Scripted Comedy (Sketch Show)' category, Please Use Other Door was picked by judges ahead of fellow nominees DMs Are Open, Gemma Arrowsmith's Sketched Out, SeanceCast, The Skewer and Thanks A Lot, Milton Jones!.
Produced by Bill Dare, the show was written by Kat Butterfield, Dan Audritt, Sophie Dickson, Laura Major, Rob Darke, Alex Nash, Sam South, Ed Amsden, Tom Coles, Cody Dahler, Toby Williams, Ed Tew, Anna Goodman, Imogen Andrews, Matt Harrison, Carwyn Blayney, Natasha Dhanraj, Alice Etches, Nathalie Antonia, Chris Ryman, Simon Alcock, Leigh Douglas, Chazz Redhead, Paul F Taylor, Jo Wiggins, Cameron Loxdale, Lewis Cook, Owen Petty, Tom Oxenham, Rebecca Heitlinger and Bill Dare.
Elsewhere during the ceremony at Broadcasting House's Radio Theatre, actor, writer and producer Martin Jarvis - whose work includes adapting the Just William novels for Radio 4 - was awarded the Lifetime Achievement title.
The BBC's Chief Content Officer Charlotte Moore says: "Huge congratulations to all the winners of the BBC Audio Drama awards. What an amazing line up of talent, and so many mesmerising performances and captivating stories. It's an extra special occasion as we're also celebrating the centenary of the unique artform that is BBC Radio Drama, which has been an important part of the BBC from the start. I'm so proud of our heritage as well as our ongoing commitment to the genre, supporting new talent and attracting the best in the industry to work across our productions."