The Argentina winger, 29, scored in each half with PSG’s Germany midfielder Julian Draxler and Uruguay striker Edinson Cavani also finding the net as the French champions tore apart a disorganised Barca side who have it all to do in the return.
PSG, eliminated by the Catalans in the Champions League quarter-finals in 2013 and 2015, were the more aggressive side at the Parc des Princes and have put themselves in a commanding position ahead of the March 8 second leg at the Camp Nou.
Five-times European champions Barca, with their trident of Lionel Messi, Luis Suarez and Neymar subdued, have not exited in the last 16 since going out to Liverpool in the 2006/07 season and the score equalled their worst Champions league loss.
“It’s impossible to have a better performance and birthday. I’m very happy with how the team played. It was a wonderful display, fully deserved,” said Di Maria, who is getting back to his best since Draxler joined form Vfl Wolfsburg last month.
Barca coach Luis Enrique said of the PSG side: “They are world class players with a lot of quality. Di Maria in particular was very, very good. They have a big attacking potential are hard in defence and incredible on the ball.
The only concern for home coach Unai Emery was the loss of the impressive Marco Verratti to a leg injury in the second half after the Italy international had put on a world class display with fellow midfielder Adrien Rabiot.