It was Tammy Abraham first goals for the club after arriving from Bayer Leverkusen for £71m earlier this month.
Ross Barkley and Olivier Giroud were also on target as the hosts eased into the fourth round at Stamford Bridge.
“I’m delighted with Kai,” said Lampard.
“It was everything I wanted the night to be for him. Because Kai has had no pre-season and signing for the club took a few days out for him as well.”
Chelsea Goals
Abraham (19’minutes)
Havertz (28’minutes, 55’minutes, 65’minutes)
Barkley (49’minutes)
Giroud (83’minutes)
Assist
Mount (28’minutes)
Abraham (55’minutes, 65’minutes)
Chilwell (83’minutes)
