The visitors opened the scoring in the first minute through Moussa Dembele, but were then swamped.
Neymar scored twice, then created the third for Edinson Cavani, before Kylian Mbappe struck before half-time.
Marco Verratti, Cavani and Dani Alves scored in a five-minute blitz in the second half to compound Celtic’s misery.
The victory was PSG’s biggest win in the Champions League, and a chastening night for the visitors, who lost 5-0 to the French giants at home earlier in the group.
The Scottish champions still have the advantage in the race to finish third in Champions League Group B – and qualify for the Europa League – with bottom-placed Anderlecht losing 2-1 to Bayern Munich.
The Parc des Princes was a blaze of colour before kick off, with the home fans as noisy as they were no doubt confident in their team. After all, PSG’s record at home is nothing short of remarkable: they had yet to concede a goal in this season’s Champions League group stages.
Yet this game was less than a minute old when Celtic spoiled that particular statistic.
Alves’ poor backpass resulted in a corner for Celtic, and the visitors took full advantage. Olivier Ntcham played a low ball to Dembele at the edge of the area, and the striker clipped a shot over PSG goalkeeper Alphonse Areola.
That was enough to send the travelling fans into raptures, but PSG were soon back on level terms.