Neymar fired Luis Enrique???s men into a first-half lead with a cool finish as the visitors dominated for large periods, before two Luis Suarez strikes put Barcelona into a commanding lead and Gregory van der Wiel pulled one back late on.
Edinson Cavani was denied by Marc-Andre Ter Stegen but the game was controlled by Barcelona, who had also earlier hit the post through Lionel Messi.
It???s a first home defeat in Europe for PSG in 34 matches, and they???re left with a mammoth task as they need to take victory at the Nou Camp next Tuesday to make it into the semi-finals.
Laurent Blanc???s men looked very edgy from the off and it was Barcelona who settled into a good early passing rhythm and tested the PSG defence with some crisp passing.
The visitors almost took a lead within the opening 15 minutes as Suarez picked the ball up on the left and chipped an excellent pass to the edge of the box for Messi, who rolled it out of his feet before curling a shot against the upright from 20 yards out.
Barcelona didn???t have to wait long to take the lead, though, as on 19 minutes they went in front. Busquets won the ball off Rabiot before it was played into Messi, and the forward released a perfect pass for Neymar, who slotted a clinical finish low into the bottom corner.
The hosts lost Thiago Silva to injury after the goal, meaning David Luiz had to be introduced earlier than planned after a surprise return to the squad from a hamstring injury.
PSG struggled to make any sort of impression on the game until after the break, when Javier Pastore drilled an effort at goal from distance, forcing Ter Stegen to parry away as it bobbled in front of the Barcelona goalkeeper.
But it was the visitors who were more clinical and Suarez opened his account on the night with a piece of individual brilliance on 67 minutes, playing the ball through Luiz???s legs before beating two more defenders and forcing a shot into the corner.
Moments later Cavani, who looked off colour for most of the game, got on the end of a loose ball and fired a volley at goal which Ter Stegen turned away superbly.
They would come to rue that missed chance as Suarez bagged his second of the night with 11 minutes remaining. The striker played a neat one-two with Mathieu before again playing it through the legs of Luiz and then firing a stunning shot into the top corner for 3-0.
PSG pulled one back two minutes later as Van der Wiel drilled a speculative effort which deflected in off the outstretched leg of Mathieu, who blocked a Cavani shot late on to keep Barcelona???s two-goal advantage intact ahead of next Tuesday???s second leg.