Trailing 4-0 after being humbled in the first leg in France, Barca returned to Camp Nou in need of a miracle.
And, after producing a sensational performance in the return meeting, they pulled off what seemed to be the impossible to put six past the French side and advance to the quarter-finals.
Neymar, however, claims that he always knew the Blaugrana would win at home and that he would play his part in turning a disastrous first-leg result on its head.
"Two of my friends said that PSG had a great team - and they did - and that they had already qualified, this and that..." the 27-year-old told DAZN.
"But I got up and said: 'You are my friends, you work with me, but it seems you don’t believe we can turn this game around. We will reverse this situation, and I promise you two goals'.
"We had trained in the morning and I saw each player’s face. Everyone was happy, nobody was down or worried about reversing the situation against PSG. We knew it would be very difficult to reverse the game.
"Our conversation was about playing football as it had always been Barcelona’s play to display good football, to turn a football game into a show.
"We knew we would win. We didn’t know if we would go through to the next round, but we knew we would win because we knew we would play our part very well.
"When the game began, it started with a different vibe. I was challenging everyone, running more than ever. It was one of, if not the biggest match I’ve ever played in and one of the most emotional.
"We scored the first two goals quickly so we were thrilled. We went into half-time 2-0 up with two more goals to score. The team we had was different - we didn’t go about screaming in the dressing room. No, it was a conversation.
"We were very calm, very focused, relaxed and the only conversation I remember having was: 'Keep calm, let’s do it goal by goal'. We were not worried about going into the next round. I think that’s why we played really well that day. We were not desperate. We were quiet and focused.
"The atmosphere after the second goal was different. We saw that the fans were believing. They kept shouting, encouraging us.
"When we scored the third goal, it was Leo [Messi] who scored. I won the penalty, he scored it. The fans were on fire and we thought: 'Let’s go, now we’re going to go through'.
"At that moment, we suffered a blow, [Edinson] Cavani’s goal. When we conceded the goal, we saw everyone was half-hearted, doing that face: 'We’re f*cked'. It became more difficult, it was practically impossible. Everyone thought we would score another, but now we had to score three.
"We still tried to keep playing our football, to continue to score goals, to see what would happen. We just hoped not to concede any more goals. One goal had already complicated things because we had to score three. Two? Forget about it.
"I still believed. I still wanted to score those two goals I promised to my friends. Oh, it gives me shivers, a lot of strong emotions definitely."
With 88 minutes gone, Neymar curled a spectacular free-kick into the top-left corner to deliver the first half of his promise and take the score 4-1 in Barca's favour, although it remained 5-4 to PSG on aggregate.
Moments later, Luis Suarez won a penalty and it was the Brazilian who was charged with the responsibility to take it.
"I was going to give it to Leo, but Leo told me to take the penalty," Neymar recalled. "He said: 'No, you go'. I said: 'Me?' He said: 'Yes, you do it'.
"My only thought was that I could not miss that penalty, because if I missed the penalty I would end the stadium’s dream of going through to the next round.
"It was the most I’ve ever focused on a penalty, and thank God I managed to score. I kept the promise of two goals. That was the moment I thought we had it. I asked Leo: 'Why did you let me take that penalty?'
"He said: 'I felt at that moment that you would score the goal, that you were more confident'. I think he had that feeling, and it turned out alright. The penalty brought the possibility, the strength, to score the sixth goal."
Only seconds remained of second-half injury time as Barca pushed for a match-winning strike and it was Neymar himself who engineered the move to send Sergi Roberto through on goal to complete one of the greatest Champions League comebacks ever.
"In that game, the most striking goal was Sergi Roberto’s," Neymar said. "It was the goal that made us go through. It’s the goal that will be remembered in history and I’m happy to have made the move, but his goal was special - that’s when the Camp Nou exploded.
"That was the most important goal. I think that, in terms of excitement, in terms of making everyone crazy, that was one of the most important goals in Barcelona history.
"I wasn’t crying, I was over the moon! It was crazy. I had never seen Camp Nou like that. After the sixth goal, the explosion was huge, both for the players and the fans. It was something that I don’t think I’ll ever live through again.
"That’s why I’ll remember it for the rest of my life."