Angel Di Maria opened the scoring at Parc des Princes on Tuesday evening, before Julian Draxler doubled the hosts' lead before the half way point.
Di Maria then netted his second and PSG's third with a curling effort from the edge of the box before top goalscorer Edinson Cavani rounded off the scoring with a fourth.
And PSG president Nasser Al Khelaifi believes that his side completed the near-impossible by humiliating the Catalan side, but has warned those below him that the job is only half done.
"We are not here to send a message to anyone," Al Khelaifi told Goal. "But it was very important to win this match and it was a fantastic win. To beat the best, with the best player in the world, Barcelona 4-0, it's very difficult - almost impossible.
"We had a fantastic match. The coach, the players, the staff, the fans - they were amazing.
"The first half has finished but there is another half. There are another 95 minutes to play which will be much more difficult than tonight, so we have to be ready.
"Tonight we're going to celebrate a little bit but then we are going to be ready."