Lionel Messi scored before succumbing to injury at half-time, and Xavi's late penalty appeared to seal the French side's fate, but Matuidi's even later strike leaves the tie open
Tito Vilanova returned to the Blaugrana dugout for the first time in months after undergoing cancer treatment in New York, but his long-awaited comeback was tainted somewhat by the departure of Lionel Messi during half-time with a hamstring injury.
But the Argentine still managed to make his mark on the game before his withdrawal, slotting home from a glorious Dani Alves assist to give Barca a narrow lead at the interval, after PSG were the more threatening side during the first 45 minutes.
The French side would controversially find a way back into the tie in the 79th minute when Zlatan Ibrahimovic turned home a rebound from an offside position, but their fortune was short-lived as Xavi scored a late penalty on the stroke of injury time.
But the drama was not done, as Blaise Matuidi struck with the last kick of the game, leaving it all to play for during the second-leg at Camp Nou in eight days' time.
David Beckham was handed a start for the hosts with Lucas Moura and Ezequiel Lavezzi also making a swift return to their XI. Meanwhile, Victor Valdes, Jordi Alba and Xavi were restored to the visitors’ starting lineup after missing out over the weekend.
Whatever nerves PSG may have felt from the indomitable reputation of their opponents were quickly shaken off during an energetic start to the match, where they could have taken the lead twice inside the opening 20 minutes.
Lavezzi was first up with a deflected effort that cannoned off the far post, before Ibrahimovic forced a world-class save from Valdes, who saw his free-kick late after it was hammered through the wall.
Barca were not without their own early opportunities, as Andres Iniesta missed by inches with a curling shot, but it was PSG who looked like prime candidates to break the deadlock, as Javier Pastore’s 25-yarder called Valdes into action again.
But PSG could not build on their positive start, and as the first-half went on, their counterattacking threat diminished as Barca’s tiki-taka football became more of a feature.
And they were made to pay for their lack of ruthlessness five minutes before half time as Messi, anonymous until that point, drilled home from an absolutely breathtaking outside-of-the-boot pass from Alves.
The Argentine could have made it 2-0 minutes later, but could not keep his shot down after racing into a fantastic position inside the area.
And that would end up being Messi’s last notable contribution of the match, as a suspected hamstring complaint forced him off during the break, with Cesc Fabregas replacing him for the second period.
But in sharp contrast to the start of the match, the second-half saw PSG struggle to get into their stride as the tempo of the game dropped markedly.
Sergio Busquets’s long range shot was smothered convincingly by Salvatore Sirigu, and Alexis Sanchez’s poor first touch denied him a clear opening inside the box as Barca just about seemed to have the upper hand.
With 11 minutes remaining, Ibrahimovic would drag PSG back into the tie in contentious fashion, as he turned home a rebound from an offside position after Thiago Silva’s header took a ricochet off the post.
But in the 90th minute, their joy turned to despair as a moment of rashness from Sirigu sent Sanchez tumbling inside the area, leaving the referee with no choice, and Xavi stepped up to bury the resulting penalty.
It seemed like the end of PSG's European ambitions for another season, but with the last kick of the game, Matuidi managed to squeeze a shot past Valdes to blow the roof of the stadium and give the French side reason to believe.