Five-time winners Barcelona have not failed to reach the last eight since the 2006/07 season but they will need to produce something special to turn this tie around after a PSG masterclass at the Parc des Princes.
Di Maria, on his 29th birthday, got things rolling with an 18th-minute free-kick and Julian Draxler doubled the home side’s advantage just before the break to leave Barca, champions in 2009, 2011 and 2015, on the ropes.
And things went from bad to worse for the Catalan giants as another fine strike from outside the box by Di Maria made it 3-0 in the 55th minute, before his fellow Argentinian Cavani added a fourth with 19 minutes to go.
It was Cavani’s 34th goal in all competitions this season and capped a memorable 30th birthday for the forward.
The result matched Barcelona’s heaviest defeat in UEFA competition and leaves Luis Enrique’s men needing one of the biggest comebacks in European history if they are to turn the tie round at the Nou Camp on March 8.
In Tuesday’s other match, Benfica edged to a 1-0 win over Borussia Dortmund in Portugal.
Konstantinos Mitroglou struck the only goal of the first leg early in the second half when he slotted home from close range after a corner had been headed towards the far post.
Dortmund had a great chance to level in the 57th minute – and earn a valuable away goal – but star striker Pierre-Emerick Aubameyang saw his penalty saved by Benfica keeper Ederson.