Having lost the first leg 4-0, Luis Enrique's men scored six times in the second leg – three of the goals coming from the 88th minute onwards – to move into the quarter-finals in the most incredible fashion.
The Camp Nou crowd could not believe what they were seeing - how did Barcelona pull it off?
Here are the key moments from a night that will never be forgotten:
3' GOAL – LUIS SUAREZ 1-0 (agg 1-4)
Barcelona got just the start they wanted and PSG dreaded, Suarez heading in from inside the six-yard box after the visitors failed to clear Rafinha's cross, with Marquinhos, Marco Verratti and Kevin Trapp all at fault.
11' PENALTY CLAIM DENIED 1-0 (agg 1-4)
PSG claimed for a penalty when Julian Draxler's cross struck the arm of a sliding Javier Mascherno from close range, but their protestations were waved away.
40' GOAL – LAYVIN KURZAWA (OG) 2-0 (agg 2-4)
PSG still looked to be in a strong position before Barca's second goal changed the tie's complexion. Andres Iniesta capitalised on a mistake from Marquinhos before his flick was sliced into his own net by defender Kurzawa. Suddenly the pressure was on the visitors.
50' GOAL – LIONEL MESSI (PEN) 3-0 (agg 3-4)
Unai Emery's half-time plans quickly unravelled when Neymar was fouled by Thomas Meunier, allowing Messi to thump home a penalty, which Trapp could not keep out despite correctly diving to his right. Now it really was game on.
52' POST – EDINSON CAVANI 3-0 (agg 3-4)
Despite trailing the second leg 3-0, PSG know an away goal should be enough to send them through. They came so close when Edinson Cavani hit the post from Meunier's cross.
62' GOAL – EDINSON CAVANI 3-1 (agg 3-5)
Cavani scored with a brilliant strike after Kurzawa headed Verratti's free-kick into his path. The celebrations from Emery and the PSG technical stuff suggested they thought the job was done.
64' SAVE – MARC-ANDRE TER STEGEN 3-1 (agg 3-5)
In a moment that became even bigger due to what followed, Ter Stegen made a crucial save from Cavani after the striker was sent clean through on goal by Draxler's pass.
66' – OFF THE LINE 3-1 (agg 3-5)
One minute after coming on, substitute Arda Turan collected Messi's pass and saw his shot cleared off the line by Marquinhos, with time now working against Barca.
76' SUB – SERGI ROBERTO ON FOR RAFINHA 3-1(agg 3-5)
Luis Enrique used the second of his changes, Roberto replacing Rafinha – but with Barca still needing three goals to progress the hosts' momentum had stalled.
85' MISS – ANGEL DI MARIA 3-1(agg 3-5)
Di Maria could not hit the target after being played through on goal by Verratti and his claims for a foul from Mascherano fell on deaf ears.
88' GOAL – NEYMAR 4-1 (agg 4-5)
After Di Maria fouled Neymar, the Brazil international stepped up himself and delivered an impressive free-kick into the top corner, although Trapp barely moved.
90+1' GOAL – NEYMAR (PEN) 5-1 (agg 5-5)
A hugely controversial moment as Suarez claimed he was pulled back by Marquinhos as he raced into the area. Referee Deniz Aytekin agreed and Neymar stepped up to send Trapp the wrong way, ensuring PSG had a nervous final few moments.
90+4' DRAMATIC DEFENDING 5-1 (agg 5-5)
In a frantic spell, Barcelona threw Ter Stegen into attack for a last-gasp free-kick after Messi was fouled by Verratti, who was booked. PSG managed to clear, but the goalkeeper retrieved possession and was fouled, with Verratti the culprit again.
90+5' GOAL – SERGI ROBERTO 6-1 (agg 6-5)
The resulting free-kick was taken short to Neymar, who dinked in a cross for Roberto to charge through and beat Trapp with a volley. Camp Nou erupted and PSG barely had time to kick off as Emery looked on in disbelief.
90+6' FULL TIME
The jubilation on the faces of Luis Enrique and his players contrasted with utter dejection in the visiting ranks, the final image from one of the most amazing comebacks ever seen on a professional football field.