Ziyech pulled out of global action for Morocco last week and missed Ajax's win over last-placed RKC Waalwijk in the Dutch league but coach Erik ten Hag said he was likely to feature in the Group H match.
A ideal hat-trick, Mbappe is now the youngest player to achieve that feat in the Champions League, doing so at the age of 20 years and 302 days.
Messi had achieved the feat aged 21 years and 288 days, who in turn had set the record besting Real Madrid legend Raul's mark of 22 years and 163 days.
Icardi had a chance to double the Paris side's advantage six minutes into the second half, but his effort across goal was well-saved by Mignolet.
Tuesday night's hosts, Club Brugge, bring an impressive and encouraging 20-match unbeaten run in all competitions into this Matchday 3 clash with French champions, PSG, so the hosts will be in confident mood that they can reduce the deficit on the Group A leaders here.
Defendant in Giuliani associates probe gets bail
As of Wednesday evening, Fruman had met the bond requirements and was no longer in the custody of the Alexandria, Virginia, jail. Two other defendants - Giuliani pals Igor Fruman and Lev Parnas - are scheduled to be arraigned before Oetken on Wednesday.
"I wanted to start, I thought I would start. I also wanted to show that it's hard to get by without me", Mbappe told broadcaster RMC Sport. Kylian also thanked the medical team of the French club that helped him recover from his injury.
Mauro Icardi netted the other two goals as fellow Argentinian Angel Di Maria directly set-up three of his side's efforts.
'I want to play every game, resume the pace and score goals. "This was not a win for Kylian, but a win for PSG".
The PSG star's hat-trick also made him the first Champions League substitute to score three times since Joseba Llorente did the same for Villarreal in October 2008 against Aalborg.
PSG have a maximum nine points, are yet to concede a goal in Europe this season and will be through to the last 16 with a win at home to Club next month. Club Brugge has two points from three games, and Galatasaray has one point.