Scots-born Capaldi was named Best TV Comedy Actor for his role as Malcolm Tucker in The Thick Of It, while Front won the Best TV Comedy Actress award for her portrayal of Nicola Murray in the political satire.
Her success meant there was no win for Olivia Colman, who was nominated in the category for two different roles - in Olympic satire Twenty Twelve and the sitcom Rev.
Capaldi saw off competition from Downton Abbey star Hugh Bonneville, who got a nod for his Twenty Twelve role, along with Tom Hollander for Rev and Steve Coogan.
Ali G and Borat star Sacha Baron Cohen won a special award for Outstanding Achievement - more than a decade after he was named Best Newcomer.
Other winners include Charlie Brooker, named Best Comedy Entertainment Personality, and Harry Hill, whose TV Burp show was named the Best Comedy Entertainment Programme.
The award for Best Sitcom saw The Thick Of It, Rev and Twenty Twelve all lose out to Julia Davis's SKY show Hunderby, which was also named Best New Comedy Programme.
The viewing public were also asked to vote for the King or Queen of Comedy with Jack Whitehall beating Alan Carr, Graham Norton, David Mitchell, Lee Mack and Sarah Millican.
The show, sponsored by Foster's, was hosted by Jonathan Ross on Channel 4 last night.
The full list of winners:
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.