Kylian Mbappe scored a first-half penalty for PSG, who were in control of the tie after winning the first leg at Camp Nou 4-1.
But the eventual 5-2 aggregate winners were second best in the return leg, as Barcelona fought hard. Lionel Messi - who has been linked with a move to PSG - scored a stunning equaliser but then had a penalty saved.
Who were some of the most notable performers, for good and bad reasons, on the night?
✔️ Lionel Messi: 8.6
The match may be remembered for his penalty miss, but Messi was otherwise excellent as Barca were eliminated.
Had he scored his spot-kick on the stroke of half-time, it would have been a tense second half for PSG. Instead, Keylor Navas got down and deflected his effort onto the crossbar and the outcome of the tie was not in doubt again from that point on.
But Barca only had an outside chance of a comeback because Messi had already produced a moment of brilliance.
He collected a pass from Pedri and unleashed an unstoppable long-range effort past Navas and into the top corner after 37 minutes.
Messi was relentless, firing in seven shots and completing four dribbles, both game highs. He played 49 passes into the final third, second only to Jordi Alba (58).
Had Ousmane Dembele (6.7) had his shooting boots on, this could have been a memorable night for Barca.
❌ Lavyin Kurzawa: 5.3
Kurzawa was replaced at half-time after giving away a penalty for a foul on Antoine Griezmann, and had previously collected a yellow card after an early infringement against Dembele.
The left-back lost four of his seven duels and had just 22 touches of the ball.
In truth, there were not many standout performers for PSG, who were cautious in the second half as they preserved their advantage from the moment Messi gave them a let off from 12 yards.
Mbappe (7.4) scored the penalty and was a constant threat on the counter-attack, but he and Navas were the only two PSG players to record a rating above 6.6.
⭐ Keylor Navas: 9.7
The former Real Madrid goalkeeper saved Messi's penalty in what was the moment of the match.
But he also did so much more in a contest Barcelona dominated.
Barca won the shot count 21-7 and had 10 attempts on target to PSG's 3, while having 72% of the possession. It took an inspired display from Navas to keep things under control.
Navas saved nine of the 10 Barca shots on target, only being beaten by an unstoppable swerving Messi strike.
He tipped a strike from Sergino Dest onto the bar having also made a key early save from Demeble.
Navas had eight saves in a memorable first half, including keeping out a powerful Sergio Busquets effort.
Having won three Champions League titles with Real Madrid, Navas will be key to PSG's hopes of going all the way.