Frank Lampard’s side have now kept three consecutive clean sheets in all competitions and new signing Edouard Mendy is still to concede a goal since joining the club.
Chelsea move up into the top four while Burnley remain bottom of the league table.
Chelsea suffered a setback 10 minutes before kickoff after Christian Pulisic pulled out with an injury and Werner replaced him.
Burnley went close to taking the lead in the opening six minutes but Mendy denied Ashley Barnes from close range.
Chelsea doubled their lead after the hour mark when Zouma converted Mason Mount‘s corner before Werner scored the third shortly afterwards.