Another birthday boy, Edinson Cavani then completed the Valentine's Day massacre with the fourth after 72 minutes, to all but put the Parisians into the last eight.
This time, the hosts, who were without injured captain and defensive stalwart Thiago Silva, succeeded in containing the Barcelona attacking trident of Lionel Messi, Neymar, and Luis Suarez.
"PSG have done what we expected and been at their best".
No side has managed to overturn a four-goal first-leg deficit in the Champions League. "They played better, they were better tactically and they outdid us physically".
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.
Barcelona got a serious taste of Verratti's and PSG's ability when the French champions beat them 4-0 in the first leg of their Champions League last-16. Also, the visitors regularly squandered possession and looked lethargic throughout.
What's up with Barcelona players and Luis Enrique?
Each of PSG's three forwards offers something different, and they complimented each other well.
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They finished the game with 16 shots on goal, 10 of those on target.
Barcelona were not given as much share of the ball as they would have liked as their strategy was cancelled out by PSG's brilliance and quick movement on and off the ball, and Paris Saint Germain further went into the comfort zone as time wore on.
PSG become the sixth team after Chelsea, Bayern Munich, AC Milan, Dynamo Kiev and Valencia to score four goals against Barcelona in a Champions League match.
It marked just Emery's second win in 24 matches against Barca, but the former Sevilla and Valencia coach said his team as a whole could take the plaudits.
At just 23, left-back Digne has already experienced the demands at the top level with PSG in his homeland and Roma in Italy, but nothing comes close to the demands he faces day-to-day since joining Barcelona in July.
Angel di Maria opened the scoring with a curling free-kick after 18 minutes when Umtiti was turned by Julian Draxler and he pulled him down. Draxler, who underperformed at Wolfsburg, has excelled since his January move to the French capital.
"They overcame our pressure and they were better with and without the ball".
The current format of Europe's elite competition, coupled with the way the UEFA Champions League is drawn, sees many clubs paired together on a regular occasions during the knock out rounds.
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