The 2-2 draw between the pair in last week's quarter-final first leg had handed the advantage to the Catalans, but with star player Lionel Messi only starting the return as a substitute due to a hamstring injury, they seemed nervous throughout and PSG deservedly went in front just after half-time through Javier Pastore.
However, with Messi summoned from the bench, Pedro fired home 19 minutes from time to send Barca into the last four.
And the winger was even more relieved to have scored the equaliser having given the ball away in the lead up to the PSG goal.
"They went ahead due to an error by me, but in the end we were able to equalise and we deserved to go through to the semi-finals," he told Canal+.
However, Pedro admitted that it was Messi's introduction that turned the game around in the final half hour.
"He made a great effort. He is very important for the team and this week he has worked his upmost to get here," he said.
"We need to thank him for his involvement. The team turned around completely with his introduction."
Even without Messi, Barca came within inches of the perfect start when Xavi curled a free-kick inches past Salvatore Sirigu's right-hand post.
Thereafter though the first-period belonged to the visitors who capitalised on Barca's uncharacteristic slackness in possession to take a stranglehold of the game, thanks in particular to the pace and drive of Lucas Moura.
The Brazilian saw a fierce strike from outside the area well handled by Victor Valdes, before he and Ezequiel Lavezzi both wastefully shot over when well-positioned.
Lavezzi then had the biggest chance of the first-half as he latched onto Zlatan Ibrahimovic's through ball, but his prodded effort lacked the power to beat Valdes who comfortably blocked with his feet.
Ibrahimovic was the provider again as Lucas saw a headed effort at the back post turned over by Valdes as the pressure from the French league leaders continued.
The goal that PSG had been threatening all night finally did arrive five minutes after the break as an excellent one-two between Pastore and Ibrahimovic sent the Argentine in behind the Barca defence and this time there was nothing Valdes could do to keep out his left-footed finish.
Pastore missed a great chance to register his second of the evening eight minutes later from another lightning PSG break, but this time he scuffed wide from 12 yards.
Dani Alves then had Barca's best chance up to that point of the evening as he blasted over when unmarked at the back post before Messi replaced Cesc Fabregas to a huge ovation.
Messi's arrival instantly forced Barca onto the front foot and, after Gerard Pique had a shot blocked, Iniesta forced Sirigu into his first serious save with Messi unable to control the rebound.
Pastore dragged another shot wide at the other end as PSG maintained a threat on the break, but the Parisians were made to rue their wastefulness in front of goal as Barca equalised on 71 minutes.
Inevitably, Messi was involved as he jinked past a couple of defenders and rolled the ball into David Villa who laid it back for Pedro to smash home.
And despite a nervy final 15 minutes for the hosts, PSG couldn't create another clear opening as Barca join Real Madrid, Borussia Dortmund and Bayern Munich in Friday's semi-final draw.
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