Barcelona manager Luis Enrique had said it was possible but few had believed him.
Unai Emery's PSG had been utterly dominant at the Parc des Princes just three weeks ago -- appearing to end this Champions League last 16 tie as a contest.
Four goals down from the first leg, Barcelona required nothing short of a sporting miracle to have any chance of coming back.
With just two minutes of regulation time remaining, Barcelona had a 3-1 lead on the night but required a further three goals to go through after Edinson Cavani's 62nd-minute strike.
A pinpoint Neymar freekick in the 88th minute might have induced Parisian nerves but it wasn't until Luis Suarez went down in the penalty area in added time that Barcelona truly believed.
Suddenly Barcelona had the chance to make it 5-1 on the night and 5-5 on aggregate. Neymar made no mistake, setting up a grandstand finish.