The 2009 and 2011 champions went in front seven minutes before half-time when Dani Alves produced an exquisite pass with the outside of his right boot straight into the path of Lionel Messi who drove the ball in with his left foot from an acute angle.
World Player of the Year Messi then sustained a hamstring injury and was replaced by Cesc Fabregas at half-time.
Zlatan Ibrahimovic gave PSG a lifeline when he scrambled in the equaliser, even though he looked offside before a soaring header from Thiago Silva rebounded to the Sweden striker off the post in the 79th minute.
Xavi calmly restored title favourites Barca's advantage from the penalty spot after goalkeeper Salvatore Sirigu rushed off his line in the 89th minute and brought down Alexis Sanchez.
Matuidi then struck with the last kick of the game when his long-range shot eluded the outstretched fingers of keeper Victor Valdes.
"The referee [German Wolfgang Stark] made some questionable calls," Barca assistant coach Jordi Roura told reporters after the quarter-final tie.
"It's a good result but it comes at a high price," Roura added, referring to the injuries sustained by Messi and defender Javier Mascherano.
Argentine Mascherano will be out for six weeks after he was carried off on a stretcher with knee ligament damage in the 84th minute.
Midfielder Matuidi was booked and will miss the second leg at the Nou Camp on April 10 through suspension.
David Beckham became the first British player to appear for four different clubs in the Champions League when he was named in PSG's starting line-up.
The former England captain did well in midfield before being taken off midway through the second half.
"I think we deserved a draw tonight," said Beckham. "There's no reason why we can't go there and get a result.
"I was very happy, the manager [Carlo Ancelotti] has always shown confidence in me. Tonight was a big moment for the club - it doesn't get much better than these nights."
PSG, unbeaten at home in all competitions since November 17, went for Barca's throat in the opening stages but were not rewarded for their efforts.
They went close in the fifth minute when Javier Pastore chested an Ibrahimovic pass into the path of Ezequiel Lavezzi who struck Valdes's right post.
Lavezzi wasted another good opportunity five minutes later, shooting straight at Valdes after collecting a brilliant through ball from Lucas.
Pastore then fired a powerful low shot that forced Valdes to dive to his right and the Spain keeper was at full stretch again when he stopped Ibrahimovic's 20-metre free-kick.
Barca only had Andres Iniesta's curling shot - which went wide - to show for their silky passing as PSG stamped their authority on the game.
Thiago Silva thwarted the dangerous Messi as the Argentine dribbled his way towards goal before Lucas released Ibrahimovic and the Swede's low shot went wide.
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