Flanker Boyce added a further score before Michael Allen scored a sensational solo effort after intercepting a wayward pass and racing clear of the Royal Grammar School defence.
RGS's Ed Harling responded with a first-half penalty but he couldn't kick-start a comeback against a well-organised King's side.
It was the first time either school had won back-to-back titles since the competition began in 2007 and RGS will be hoping to end that run when the two sides meet again next season.
