But no fans were in the stadium to witness the achievement.
Having lost 1-2 in the first leg, Neymar and Juan Bernat scored before half-time to secure a 3-2 aggregate win for PSG after a game played behind closed doors.
This was due to the coronavirus, which has infected 2,281 people and killed 48 in France.
The result eased painful memories of 2017, when PSG were eliminated 6-5 on aggregate by FC Barcelona after letting slip a 4-0 advantage.
Also, last season they lost to Manchester United on away goals after a 2-0 win at Old Trafford.
The French champions reached the last eight for the first time since 2016 as Borussia Dortmund finished with 10 men following Emre Can’s sending-off in the dying minutes.
Over 3,000 ultra fans gathered near the Parc des Princes before kick-off, after being granted authorisation by the police.
Demonstrations were 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 2,281 people and killed 48.
They lit firework and their chants could be overheard in the stadium before, during, and after the game as the players went to the top of the Auteuil stand to cheer with them.
“Our only virus is Paris SG,” a banner in the empty arena read.
“It was a perfect game,” said centre back Marquinhos, who with Presnel Kimpembe marshalled the PSG defence.
“We now need to keep the same mindset for the remainder of the competition.”
PSG were without captain Thiago Silva, who had not fully recovered from a hamstring injury, while Kylian Mbappe started on the bench after suffering from a sore throat.
The French side dominated possession and had the first clear chance when Edinson Cavani’s cross shot from Di Maria’s through ball was deflected by goalkeeper Roman Buerki.
Neymar put the hosts ahead in the 28th minute as he headed home Angel Di Maria’s free-kick for his 35th goal in 57 matches.
He made his presence count with this, after missing the return leg against Manchester United through injury last season.
PSG pressed high after the break while Erling Haaland, who scored a double in the first leg, never looked likely to add to his 10 UEFA Champions League goals this season.
Thorgan Hazard and Axel Witsel made way for Julian Brandt and Giovanni Reyna as Borussia Dortmund coach Lucien Favre looked to freshen up his attacking line.
(PSG) were suddenly on the back foot.
A brawl erupted two minutes from time after Can fouled Neymar and pushed the Brazilian to the ground.
Can was sent off while Di Maria picked up a yellow card which means the Argentine will be suspended for the first leg of PSG’s quarter-final.