Sam Oliver and Shishir Patel created the ad, called "polite", in which a man, who has gorged himself on Popcorn Chicken before a visit to his grandmother's house, reacts violently when he is repeatedly offered a slice of homemade cake.
The judges for the September awards, which are run by the Radio Advertising Bureau and supported by Campaign, were Axel Chaldecott and Steve Henry of HHCL & Partners.
They said: "The KFC ad is so funny, it's bound to get complaints and get pulled off air. Like a lot of successful humour, it's inherently cruel, which is great."
The ad was produced by Charlotte Lawrence through Saunders & Gordon.
The sound engineer was Ben Leeves. Media was planned and bought by Nadine Young at Zenith Media.
This month's runners-up were for NatWest and Barclaycard Premiership.
The NatWest ad, called "call centre", was created by Will Bates and Duncan Timms from M&C Saatchi.
The Barclaycard Premiership ad, "antiques show", was created by Ben Wade and Louise Almgren for BMP DDB. The ad features two workers unenthusiastically discussing an antiques show because, with the football season yet to start, there is nothing else to talk about.