Palmer scored with his left foot, head and right foot to complete a perfect hat-trick and give Chelsea a three-goal before the half-hour mark.
Nicolas Jackson added his name to the scoresheet in the 44th minute, before Palmer dispatched his second-half penalty to pile the misery on Sean Dyche's side.
Chelsea academy product Alfie Gilchrist then came off the bench to score his first senior goal and cap off a dominant performance from the home side.
Palmer's record-break performance
Not only did he fire his side to all three points, but Palmer managed to set a couple of new records with his match-winning performance.
Palmer registered Chelsea's quickest-ever Premier League hat-trick with his first three goals arriving inside the opening 29 minutes.
After scoring three times in Chelsea's 4-3 home win over Manchester United earlier this month, Palmer has put himself alongside Didier Drogba as the only two players to score in back-to-back Premier League home matches for the West London club.
The England international has also become the first Chelsea player to score in seven consecutive Premier League home appearances.
Race for the Golden Boot
Palmer has thrown his name into the mix for the Golden Boot Award following his clinical performance in Monday's victory.
Having scored 20 times in 28 league appearances, the youngster is sitting at the top of the scoring charts alongside his former Manchester City teammate Erling Halaand.
The pair have scored once more goal than Aston Villa's Ollie Watkins, while they are three goals clear of Newcastle United's Alexander Isak, Liverpool's Mohamed Salah and Bournemouth's Dominic Solanke.
Palmer is looking to become the first Chelsea player to win the prestigious prize since Didier Drogba won the Golden Boot with 29 goals in the 2009-10 Premier League season.
Mauricio Pochettino will hope Palmer can play another decisive role when his side face Man City in Saturday's FA Cup final at Wembley.