They lead second-placed Bayern Munich, who won 2-1 at Anderlecht, by three points before they play in Germany with Group B's first place at stake.
Celtic got off to a dream start when Dembele opened the scoring in the first mninute from a corner, but PSG reacted swiftly.
Neymar levelled with a low shot after being set up by Adrien Rabiot and doubled the tally in the 22nd after a one-two with Verratti.
Cavani made it 3-1 six minutes later from close range with Mbappe adding another in the 35th from Marquinhos's cross.
The Uruguayan striker, Verratti and Alves scored again after the break as PSG became the most prolific team in the Champions League group phase with 24 goals.
(Reporting by Julien Pretot; Editing by Ian Chadband)
