Andres Iniesta and Lionel Messi combined to set up Neymar for a slick opener in the 18th minute, and Luis Suarez added two brilliant strikes in the second half to seemingly seal matters.
Gregory van der Wiel’s effort was deflected past Marc-André ter Stegen by Barca substitute Jeremy Mathieu to give PSG some hope late on, but Laurent Blanc’s side have it all to do in next Tuesday’s second leg at the Nou Camp.
PSG had the first sight of goal in the eighth minute and Blaise Matuidi’s low cross from the left looked perfect for Javier Pastore, but the ball hit the Argentinian’s standing foot as he attempted to shoot and the danger was averted.
The visitors went close five minutes later when Suarez found Messi on the edge of the box. The Argentina captain made room to bend a fine left-footed effort goalwards, but saw it come back off Salvatore Sirigu’s left post.
Barca did not have to wait too much longer to open the scoring, however, as a swift break culminated in Messi playing a neat pass to Neymar, who took a touch to steady himself and then slotted calmly past Sirigu.
David Luiz made a surprise appearance from the bench in the 21st minute after his Brazil teammate Thiago Silva sustained an injury. Blanc had said on April 7 that Luiz was likely to face four weeks on the sidelines with a hamstring problem.
Luiz was dispossessed by Suarez three minutes before half-time on the left side of the PSG box, but Sirigu spared the centre-back’s blushes.
Pastore warmed the gloves of Ter Stegen with a long-range attempt at the start of the second half, but the Barcelona keeper was not unduly troubled.
PSG, without the suspended Zlatan Ibrahimovic, struggled to test the Catalan giants, and found themselves two goals down midway through the second half thanks to Suarez’s virtuoso effort.
The Uruguay frontman received the ball on the right, cut inside Luiz, held off Marquinhos and Maxwell and then beat Sirigu at his near post, the PSG keeper getting his left hand to the ball but unable to prevent it nestling in the bottom-right corner.
Edinson Cavani went close to pulling a goal back with a volley, but it was parried away for a corner by Ter Stegen.
Messi then almost added a third 17 minutes from time with a typically mazy run to the edge of the box, but for once was let down by a wayward finish.
Barca’s third goal arrived in the 79th minute, Suarez nutmegging Luiz to race free, before despatching a superb curling shot beyond a stunned Sirigu.
The home fans had something to cheer three minutes later when Jordi Alba’s defensive header was blasted back into the danger area by Van der Wiel, with Mathieu’s intervention sending it past a helpless Ter Stegen.
PSG could have cut the arrears soon after, but Adriano did enough to put off Pastore and Cavani’s shot was well blocked by a sliding Mathieu.
Sirigu, Van der Wiel, Thiago Silva (Luiz 21), Marquinhos, Maxwell, Rabiot (Lucas Moura 65), Cabaye, Matuidi, Lavezzi, Cavani, Pastore.
Ter Stegen, Montoya (Adriano 80), Pique, Mascherano, Jordi Alba, Rakitic (Mathieu 74), Busquets, Iniesta (Xavi 53), Messi, Suarez, Neymar.
Mark Clattenburg (Tyne & Wear).