Xavi's late penalty looked to have handed Barca a crucial advantage ahead of the second leg at Camp Nou on April 10, with Zlatan Ibrahimovic's controversial equaliser 11 minutes from time cancelling out Lionel Messi's sublime opener, only for Matuidi's shot to beat Victor Valdes in the last of four added minutes.
PSG coach Carlo Ancelotti named former England captain David Beckham in his starting line-up in a deep central midfield role, while Barcelona welcomed Tito Vilanova back onto their bench following his time away from the club undergoing treatment for cancer.
The home side made an excellent start and were inches away from taking the lead with only five minutes on the clock as Ezequiel Lavezzi collected possession inside the Barcelona box and saw his effort loop over Valdes before going back into play off the base of the post.
PSG continued to press and Valdes was called into action once again in the 18th minute when Ibrahimovic drilled a low free-kick from the edge of the box, awarded for Gerard Pique's foul on the Sweden striker, past the wall with the keeper plunging to his right to push it away.
Ibrahimovic will feel he should have done better midway through the half when a lightning counter-attack from the excellent Lucas Moura found the talismanic forward in space, but he dragged his shot wide of the target.
And the hosts were made to pay for their missed opportunities when Barcelona struck with rapier-like precision in the 38th minute. Dani Alves produced an outrageous pass with the outside of his boot, which most players would not even attempt, never mind execute, and Messi provided the first-time finish across Salvatore Sirigu.
Messi was inches away from making it 2-0 before the break when he cut in from right and unleashed a curling left foot effort which whistled inches away from the angle of post and bar, only to spend the remainder of the half clutching the back of his right leg, with the Argentine ace replaced by Cesc Fabregas at the interval.
Matuidi was cautioned in the 65th minute for a challenge on Andres Iniesta which will rule him out of the second leg before Alves whistled a free-kick narrowly wide of Sirigu's goal with the keeper scrambling across his line.
Beckham's night ended when he was replaced by Marco Verratti with 20 minutes to go, while Javier Mascherano was booked for felling substitute Jeremy Menez, and he will also miss the return meeting. Valdes was then called into action again to deny Ibrahimovic in a one-on-one as Mascherano and Jordi Alba were on the deck after clashing as they cleared a corner.
Barca were briefly forced to play on with nine but had their full complement back on the field when Ibrahimovic levelled with 11 minutes to go, hooking home the rebound after Thiago Silva's header had come back off the inside of the post, although replays showed he was in an offside position.
The celebratory atmosphere in the Parc des Princes was briefly silenced with time running out as Sirigu brought down Alexis Sanchez and Xavi stepped up to send the goalkeeper the wrong way, but with just seconds remaining Valdes allowed Matuidi's shot from Ibrahimovic's knock-down to squirm beyond him and over the line.