Angel di Maria scored twice as Paris St-Germain stunned Barcelona to leave the Spanish side in danger of failing to reach the Champions League quarter-finals for the first time in a decade.
PSG dominated this last-16 first-leg tie throughout and took the lead through Di Maria's curled free-kick.
Julian Draxler added a second with an angled drive before Di Maria curled an effort into the top corner.
Edinson Cavani then sealed a famous win with a powerful fourth.
A lacklustre Barcelona - with Lionel Messi, Luis Suarez and Neymar largely anonymous - did not produce an effort of note until seven minutes before the end when Samuel Umtiti headed onto the post.
The defeat leaves Luis Enrique's side with an almighty task to stay in the competition when they host PSG in the return leg on 8 March.
No side has managed to overturn a four-goal deficit in the history of the Champions League.
A brutal beating for Barca as Messi goes missing
Barcelona breezed into the knockout stage by topping Group C, winning five of the six games they played.
Their one defeat was also the only time they conceded three goals in a group-stage game, when they lost 3-1 at Manchester City.
At least in that match they managed to score - Messi putting them ahead at Etihad Stadium - but at the Parc des Princes on Tuesday they barely troubled Kevin Trapp in the PSG goal.
The visitors regularly squandered possession and looked lethargic throughout. When they have not been at their best in the past, their star players have stepped up. But on this occasion they offered nothing.
Messi, so often capable of creating something from nothing, made uncharacteristic mistakes and was at fault for PSG's second when he lost the ball to Draxler, who then played a one-two with Marco Verratti to slice through a static defence and put the French side in control.
It was one of the worst Barcelona performances in recent memory but PSG were also at their absolute best and, in truth, could have won by an even bigger margin.
They finished the game with 16 shots on goal, 10 of those on target.
Barca's joint-heaviest defeat - the stats
Paris St-Germain became the sixth team to score four goals in a Champions League game vs Barcelona (after Milan, Dynamo Kiev, Valencia, Chelsea and Bayern Munich).
Indeed, this was Barcelona's joint-heaviest defeat in the competition (0-4 vs Milan in 1994, Dynamo Kiev in 1997 and Bayern Munich in 2013).
Angel Di Maria has scored four goals in the Champions League this season - his best return in a single campaign.
Only Lionel Messi (10) has scored more goals in the Champions League this season than Edinson Cavani (seven).
No side has ever turned round a 4+ goal deficit to progress in a Champions League knockout tie.
Barca faced 10 shots on target vs PSG - their joint-highest in a Champions League match since 2003-04 (also vs Bayer Leverkusen in December 2015).