Lionel Messi gave Barca a half-time lead before departing with a hamstring injury at the interval.
Zlatan Ibrahimovic controversially equalised against his former club, before a late penalty from Xavi looked to have secured a first-leg lead for Barcelona.
However, with the last kick of the match a deflected shot from Blaise Matuidi secured a surprise draw for the French side.
And afterwards Carlo Ancelloti, the PSG coach, said his side already knew what they had to do at the Nou Camp.
"Tonight's game was pretty clear to me," he said.
"Against Barcelona you have to defend because they dominate possession but when you have the ball you need to make the most of it."
PSG put Barca under pressure in the opening half-hour and David Beckham, the first British player to represent four clubs in the Champions League, excelled in a holding midfield role.
"His ability to play forward passes was key," Ancelotti said of the 37-year-old former England captain's performance.
"He played really well with good passes."
Although the first chance fell to PSG in the opening minutes, it was Messi who would open the scoring with seven minutes remaining of the first half.
Alves curled a staggering pass into the box with the outside of his right foot and Messi ran on to the ball and fired first time inside the far post.
The Argentinian curled another effort millimetres over the bar but appeared to tweak his right hamstring in the process and was a passenger as half-time approached.
PSG looked to pressurise their opponents in search of an equaliser, which came after Javier Mascherano brought down Jeremy Menez for a free kick. The attempt was deflected behind and the resulting corner caused chaos.
Jordi Alba and Mascherano collided and were both prone in the six-yard box, playing three PSG players onside as the half-cleared set-piece was returned into the box, and Valdes was forced into a point-blank save from Ibrahimovic's shinned effort.
Barca had to defend the next corner with nine men and the controversy continued even after the pair returned, Thiago Silva heading Menez's free kick against the post before the rebound was jabbed home by an offside Ibrahimovic.
Mascherano was carried off minutes later after suffering knee ligament damage which will likely sideline him for the next six weeks.
With a minute of regulation time remaining, Sirigu was booked for pulling down Sanchez and Xavi sent the keeper the wrong way from the spot- but there was still late drama to come.
Ibrahimovic nodded the ball back and Matuidi's shot was squeezed between the legs of substitute Marc Bartra, wrong-footing Valdes and levelling the scores.
The controversy over Ibrahimovic's equaliser left Jordi Roura, the Barcelona assistant coach, unhappy.
"The referee (German Wolfgang Stark) made some questionable calls," he said after the match.
"It's a good result but it comes at a high price."
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