The win kept up their 100% record in Group A with the French team on nine points at the halfway mark and on the cusp of qualification for the next phase, a comfortable five points ahead of second placed Real Madrid.
Mauro Icardi put PSG into a seventh minute lead but it was only after World Cup winner Mbappe, working his way back after a hamstring injury, came on early in the second half that they clicked into gear.
PSG's opener was simply done with a long ball over the top from skipper Thiago Silva to find Angel di Maria, who in turn slipped a square pass for his fellow Argentine to convert.
Mbappe came on shortly after halftime and within nine minutes had PSG further ahead.
His quick footwork set up Di Maria for a square pass that Brugge goalkeeper Simon Mignolet got a hand to, serving only to pop it up in the air for a quick-thinking Mbappe to head back over him and into the net.
Mbappe then set up the third for Icardi two minutes later after a defensive slip.
Di Maria was again the provider as Mbappe made it 4-0 in the 79th minute and then completed his hat-trick four minutes later.
On both occasions it was the pace of the 20-year-old in carving his way past the Brugge defence and his deft finishing that underlined his prowess.
Club Brugge have two points from their three group games and go to Paris for their next Champions League match on Nov. 6. (Reporting by Mark Gleeson in Cape Town; Editing by Christian Radnedge)