Trailing 4-0 after the first leg of the last-16 tie, many pundits had put a line through Barca's name, but the Spanish champions pulled off the great escape with a stunning last-gasp 6-1 victory at Camp Nou on Wednesday.
Barca left it late to seal a remarkable 6-5 aggregate triumph and a spot in the quarter-finals after scoring three goals from the 88th minute onwards, having watched PSG star Edinson Cavani net an away goal just past the hour mark to seemingly end their hopes, with the hosts requiring another three to progress.
But Barca dug deep to defy the odds, with Neymar curling in a free-kick and converting a controversial 91st-minute penalty before the Brazilian star teed up Sergi Roberto for the winner five minutes into stoppage time.
Struggling to sum up the greatest comeback in the history of the Champions League, outgoing coach Luis Enrique told reporters: "It is hard to explain with words because it was like a horror film.
"There was a spectacular start; there was only one match with more tension that I've been involved in, and that was when I was a player.
"This was a victory for our faith and belief. We took risks and we assumed those risks. At half-time we spoke about scoring a third and we did.
"But then Cavani scored. Again the players showed their belief, the Camp Nou fans did too. Usually people leave 10 minutes before the final whistle. Nobody left early.
"I said six goals in the pre-match press conference because Paris are a quality team and capable of scoring. We had the evening we all wanted and we are still in the competition.
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"This is a crazy, unique sport. Children, and adults, here will never forget what happened here. I dedicate this win to all Barca fans who kept faith in us. We were massively criticised after the first leg."
Luis Enrique added: "We got over the trauma of what happened on Valentine's Day in Paris and we had nothing to lose because we'd already lost everything in Paris.
"We made tactical changes and proved we had the quality to turn the situation around. We always had two players open to play the ball to and the players executed the game plan to perfection, performing with huge desire."