Glasgow-born Capaldi was named Best TV Comedy Actor for his role as foul-mouthed spin doctor Malcolm Tucker while Front won the Best TV Comedy Actress award for her portrayal of hapless politician Nicola Murray.
Capaldi said he was delighted to win as it proved he was funny to his teenage daughter, who continually tells him: "Dad, you're so not funny".
The 54-year-old, beat Downton Abbey star Hugh Bonneville, nominated for his Twenty Twelve role, Tom Hollander for Rev and Steve Coogan, to the award.
Ali G and Borat star Sacha Baron Cohen won a special award for Outstanding Achievement more than a decade after he won the award for Best Newcomer.
Charlie Brooker was named Best Comedy Entertainment Personality, while the Best Sitcom award saw The Thick Of It, Rev and Twenty Twelve lose to Julia Davis's SKY show Hunderby, which also won Best New Comedy Programme.
The viewers voted Jack Whitehall the King of Comedy.
The show, in London, was hosted by Jonathan Ross.
AND THE WINNES WERE...
:: Best Comedy Entertainment Personality – Charlie Brooker
:: Best Sitcom - Hunderby
:: Best Male TV Comic – Lee Mack
:: Best Comedy Entertainment Programme – Harry Hill's TV Burp
:: Best Comedy Breakthrough Artist – Morgana Robinson
:: Best TV Comedy Actress – Rebecca Front
:: The Writers Guild of Great Britain – Vic Reeves and Bob Mortimer
:: Best TV Comedy Actor – Peter Capaldi
:: Best Female TV Comic – Jo Brand
:: Best Sketch Show – Cardinal Burns
:: Best New Comedy Programme – Hunderby
:: Outstanding Achievement – Sacha Baron Cohen