Chelsea played out a disappointing 0-0 draw against Fulham at Stamford Bridge on Friday night.
Potter handed new signings, Mykhailo Mudryk and Enzo Fernandez their first starts for Chelsea.
Ziyech also started after having a deadline day move away from Chelsea denied due to technology error.
Reece James made a return after missing out for weeks due to a troublesome knee injury.
Fulham were clearly the better side in the first half with Chelsea failing to have a shot on target at Stamford Bridge.
The visitors threatened through the likes of Willian, Mitrovic and Pereira but they couldn’t find the breakthrough.
Havertz’s late effort in the first half hit the cross bar.
Chelsea improved in the second half with some decent chances.
Substitute David Datro Fofana had a good effort blocked after beating Leno and Diop.
The Blues have now kept three consecutive clean sheets in the Premier League.
Fernandez impressed in his first start for his new club but he could not help secure the maximum points.
Fulham moved up to sixth on the log, while Chelsea sit in the ninth position following an underwhelming campaign.