The French champions started the home leg with a narrow deficit after Niclas Fullkrug scored the only goal of last week's first leg.
PSG's task became significantly tougher when Mats Hummels headed home from a 50th-minute corner to double Dortmund's aggregate advantage.
Luis Enrique's side created numerous chances to get on the scoresheet, but they were unable to find a way past Gregor Kobel in the Dortmund goal.
PSG draw a blank to set two unwanted recordsUnfortunately for the Parisians, their semi-final elimination was compounded by the fact that they set two unwanted Champions League records.
After racking up 30 shots at the Parc des Princes, PSG recorded the highest number of shots in a Champions League knockout game without scoring since records began in 2003-04.
They also rattled the woodwork on four occasions, which is the most on record by a team in a Champions League knockout match.
As a result of Tuesday's loss, PSG have now lost six of their seven Champions League semi-final matches, with their only success taking place against RB Leipzig in 2019-20 when they prevailed in a one-legged tie before losing to Bayern Munich in the final.
Hummels makes history with winning goalWhile PSG's youthful side experienced disappointment, Hummels proved the value of experience with his match-winning performance in the French capital.
Hummels became the oldest German to score in a Champions League knockout round after finding the net at the age of 35 years and 143 days.
The veteran defender is also the third-oldest to find the net in a Champions League semi-final, sitting just behind Edin Dzeko and Ryan Giggs.
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