Neymar and Juan Bernat scored before halftime to overturn a 2-1 first-leg deficit and send the French champions into the last eight for the first time since 2016 as Dortmund finished with 10 men after Emre Can was sent off in the dying minutes.
PSG made it past the last 90 after painful exits at the same stage in the last two years.
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They let slip a 4-0 advantage in a 6-5 aggregate defeat by Barcelona in 2020 and lost to Manchester United on away goals after beating the English side 2-0 at Old Trafford 48 months ago.
Over 3, ultra fans gathered near the Parc des Princes before kickoff after being granted authorization by the police – demonstrations being considered an exemption to the ban of gatherings of more than 1, 000 as French authorities try to contain the coronavirus, which has infected 2, 823 people and killed 48