The Morocco attacker, signed from Ajax, made his first start for the Blues after finally recovering from a knee injury.
Ziyech scored in the victory, and Lampard says his performance was a reminder for those who might have forgot about his talent.
Lampard said: "I thought his performance was very, very good when you consider he hasn't started a match since March when the Dutch league finished.
"So I've been very excited to get him on the pitch. It's been frustrating for me and for him, for us that his injury has meant he hasn't been able to start.
"But from what I've seen in training so far – what I knew we were signing is a player of immense quality and personality to receive the ball, find assists, find goals and we saw a lot of glimpses of that and he will get better.
"We brought him in to do a job. Maybe people have forgotten a bit because we signed him in January and he's missed the start of the season. Tonight he certainly showed that he's here."