With Thursday's (AEDT) clash at Parc des Princes played behind closed doors amid fears over the spread of coronavirus, PSG overturned a 2-1 opening-leg deficit to progress to the last eight for the first time since 2016.
Neymar got Thomas Tuchel's side started in the 28th minute, capping an impressive display with a diving header from point-blank range, before Juan Bernat doubled PSG's tally.
And with Dortmund toiling to claw their way back into proceedings, their frustrations were compounded in the closing stages – Emre Can seeing red for becoming embroiled in an off-field scuffle as Lucien Favre's side dropped out with a whimper.
With thousands of fans making their voices heard outside Parc des Princes, it was Dortmund who went close to a breakthrough against the run of play – Erling Haaland inches away from connecting with Achraf Hakimi's cross.
It was PSG's turn to rue a glorious chance in the 25th minute – Edinson Cavani racing through on goal only for Roman Burki to make a superb save with his right foot.
But Burki was beaten three minutes later, Neymar left unmarked in the six-yard box to head in from Angel Di Maria's corner.
Jadon Sancho tested Keylor Navas as Dortmund looked to respond, yet PSG turned the tie further in their favour on the stroke of half-time when Bernat diverted home.
Di Maria's long-range free-kick had Burki lunging to his right nine minutes after the restart, before Tuchel introduced Kylian Mbappe, who had been a doubt due to a throat infection.
Dortmund substitute Julian Brandt had more of an impact, though his deflected strike onto the roof of the net was the closest the visitors came to keeping themselves in the competition before Can's red card for violent conduct all but ended their slim hopes.