PSG host relegation battling Le Havre on Saturday
Messi finally got his first assist of the season when he picked out defender Clement Lenglet with a splendid cross and the Frenchman rose to head Barca in front after 21 minutes.
The Argentine also had a hand in Barca's second goal, laying on a pass for rightback Sergino Dest to latch on to down the right flank and play a cross into the path of Martin Braithwaite, who slid in to score in the 35th minute.
Record-breaking Messi capped a brilliant individual and team display with a splendid goal of his own midway through the second half, running in behind to meet a pass from teenager Pedri and slotting the ball into the far bottom corner.