Holy messenger di Maria scored twice as Paris St-Germain paralyzed Barcelona to leave the Spanish side in risk of neglecting to achieve the Champions League quarter-finals without precedent for 10 years.
PSG overwhelmed this last-16 first-leg tie all through and led the pack through Di Maria's twisted free-kick.
Julian Draxler included a moment with a calculated drive before Di Maria twisted an exertion into the top corner.
Edinson Cavani then fixed a well known win with an effective fourth.
A dreary Barcelona - with Lionel Messi, Luis Suarez and Neymar to a great extent mysterious - did not create an exertion of note until seven minutes before the end when Samuel Umtiti headed onto the post.
The annihilation leaves Luis Enrique's favor a god-like undertaking to remain in the opposition when they have PSG in the arrival leg on 8 March.
No side has figured out how to upset a four-objective first-leg shortfall in the historical backdrop of the Champions League.
A brutal beating for Barca as Messi goes missing
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.
Are PSG serious contenders?
They have never progressed beyond the quarter-finals but dominant wins home and away against Chelsea at this stage of the competition last year suggested they had finally joined the continent's elite, only for them to then lose against Manchester City.
Unai Emery, PSG's Spanish manager, had faced Barcelona 23 times before in his coaching career and won just once.
But Emery has form in Europe. He led Sevilla to three successive Europa League titles from 2014, getting the best of the players at his disposal and that is proving to be the case at PSG.
Cavani now has 34 goals in 32 matches while Di Maria is producing consistently what he only managed in flashes at Manchester United. Draxler, who underperformed at Wolfsburg, has excelled since his January move to the French capital.
All three were key to Barcelona's downfall and this could prove to be a watershed moment for both PSG and Emery.
"I think this makes PSG a threat in the competition," former Manchester United defender Rio Ferdinand told BT Sport.
"Mentally they will go on again and they will believe now they are capable of winning this tournament by beating one of the best teams."
Home form hope for Barcelona
Barcelona were one of the favourites to win the Champions League at the start of the season but will now need to produce one of the greatest comebacks in football to stay in the competition.
They are more than capable of scoring goals for fun at the Nou Camp, having hit three or more in six of their previous seven games.
Borussia Monchengladbach were the last side to visit Barcelona in the Champions League and they lost 4-0 in December.
It is sure to be one of the toughest tests of Enrique's Barcelona career to date.
Man of the match - Angel di Maria
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).
This is dummy text. It is not meant to be read. Accordingly, it is difficult to figure out when to end it. But then, this is dummy text. It is not meant to be read. Period.
ConversionConversion EmoticonEmoticon