The Premier League outfit were the better side throughout and raced into a commanding lead thanks to quick-fire goals from Daniel Sturridge and James Milner.
However, Thomas Meunier brought PSG back into it before the break, before Kylian Mbappe struck seven minutes from the end to draw them back level.
Nevertheless, there was to be another twist in the tale as substitute Firmino won it at the death.
With PSG only half clearing a Xherdan Shaqiri corner, the ball was won back in midfield and fed out to Firmino on the right-hand side of the box.
He cut in and then outside of his man to create a yard of space before driving home low into the far corner to secure a dramatic win.