Frank Lampard's side have now kept four 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.
"It was a very complete performance from us," Lampard said postmatch. "We controlled massive parts of the game, so I'm very happy.
"Performances like this show that we're doing something positive. We need to get our heads down and keep working hard," he said.
Burnley's winless start has them stuck at the bottom of the table after their opening six games but manager Sean Dyche said there is no question of his team panicking.
"I don't panic in general, to be honest, I'm not that sort of fella," he said. "I don't think panicking will change anything. I think structure, organisation and hard work, that may change things."