Coming into the second leg with a 3-2 advantage from their victory in the French capital, the La Liga champions extended their chasm early doors through Raphinha, but what followed can only be described as a calamitous implosion from Xavi's side.
After losing Ronald Araujo to a first-half red card, Barcelona were powerless to quell a barrage of attacks from Luis Enrique's team, as Ousmane Dembele and Vitinha struck before a Kylian Mbappe double kept the visitors' dreams of a long-awaited maiden European title live.
With nothing but a win good enough to avoid yet another premature Champions League elimination, PSG started strong in Catalonia, where ex-Barca winger Dembele was booed with every touch of the ball.
As Dembele felt the wrath of the home crowd, his successor - Lamine Yamal - felt the love from the Blaugrana faithful, as with 12 minutes gone, the 16-year-old acted as the architect for Barca's first strike of the evening.
Squaring up to the intimidating Nuno Mendes out wide, Yamal beat the Portuguese full-back all ends up with a neat shift out to the byline before cutting back for the arriving Raphinha, who directed the ball into the net via his shin.
The ex-Leeds United man seemingly knew little about it, but his darting run to the near post was rewarded, while PSG's mountainous task became even more difficult after their quick start petered out.
However, Enrique's men received a huge leg-up from referee Istvan Kovacs in the 29th minute, as Ronald Araujo clipped the surging Bradley Barcola from behind as the Frenchman burst into the box and took the walk of shame for his troubles.
The contact took place just outside the Barcelona area, but Kovacs did not hesitate to brandish the red card for the Uruguayan defender, whose fierce protestations that Pau Cubarsi was covering on the other side fell on deaf ears as Barcelona went down to 10.
Dembele failed to make the most of the free kick, but after Frenkie de Jong briefly filled in as an emergency centre-back, Xavi saw fit to sacrifice the unhappy Yamal for Inigo Martinez to beef up his decimated backline.
The Blaugrana rearguard unsurprisingly came under siege from a reinvigorated PSG, who reduced their aggregate deficit and got back on level terms on the evening with five minutes of the first half remaining.
The recalled Barcola whipped in a terrific low ball from the left, which Mbappe could not connect with, but Barca's public enemy number one Dembele was ready and waiting at the back post to fire home into the roof of the net.
Mbappe and Martinez were both booked for a fracas in the aftermath, and Dembele nearly burned more bridges with the home crowd in the third minute of added time, side-footing a volley just wide of the far post before the half-time whistle arrived for a beleaguered Barcelona.
Normal service resumed at the start of the second period, where Fabian Ruiz was the next to send a strike a whisker wide in the 52nd minute, but his midfield colleague Vitinha made no mistake just two moments later.
A short corner routine was worked out to the Portuguese midfielder, who was invited to shoot as Barcelona failed to close him down, and he punished the hosts with an arrowed 20-yard strike into the far corner.
Vitinha's tie-levelling strike sparked unbridled bedlam on the field, as Ilkay Gundogan struck the outside of the post almost straight from kickoff, before Barca head coach Xavi also saw red for kicking the protective padding around a camera man's booth after a free kick went against his side.
The 44-year-old's rage meter would not have decreased on the hour mark, as Joao Cancelo's nonsensical challenge from behind on Dembele saw referee Kovacs immediately point to the spot; Mbappe's postage-stamp strike was out of Marc-Andre ter Stegen's reach as PSG went ahead on aggregate.
There was still some life in a dumbstruck Barcelona, whose talisman Robert Lewandowski was thwarted by a strong low save from Gianluigi Donnarumma in the 73rd minute, before an amazing intervention from all-time appearance maker Marquinhos prevented Ferran Torres from poking in the rebound.
However, there was no way through an inspired PSG backline, and the final nail was hammered into the Barcelona coffin in the 89th minute, where a Parisiens counter-attack ended with Ter Stegen producing two fine saves from Mbappe and Marco Asensio, but a sliced Jules Kounde clearance fell kindly for the former to crash home the clincher at the near post.
Devastated Barcelona fans began to head for the exits as Ter Stegen's strong injury-time save denied Mbappe his hat-trick, but there was no stealing the PSG thunder, as the overjoyed French champions set up an intriguing semi-final showdown with Borussia Dortmund owing to the German side's own stunning turnaround against Atletico Madrid.
As for the Spanish champions, Tuesday's agonising loss marked their first reverse since Xavi announced his decision to step down as head coach, and things do not get any easier for La Blaugrana, who now have Sunday's El Clasico with Real Madrid to prepare for.