Lionel Messi gave Barca a half-time lead, a goal owing much to Dani Alves' vision, before departing with a hamstring injury at the interval.
Zlatan Ibrahimovic controversially equalised against his former club and though Xavi's late penalty looked to have ensured a first-leg lead for Barca, Blaise Matuidi made it 2-2 with a deflected last kick of the match.
The first chance fell to Paris Saint-Germain with less than five minutes played. Ezequiel Lavezzi cut inside, sending Gerard Pique sliding the wrong way, and Barca midfielder Sergio Busquets stuck out a foot to stab the ball against the frame of his own goal.
Alex climbed highest to meet David Beckham's corner but headed well wide, and Victor Valdes then dived to save Javier Pastore's low drive and had to scramble to recover the loose ball ahead of the onrushing Alex.
It added up to an opening 15 minutes of PSG dominance, though Andres Iniesta soon curled just wide at the other end.
PSG pressed again and when Pique flattened Ibrahimovic just outside the 'D' and was booked, Valdes had to push the Swede's fierce low free-kick around the post.
Ibrahimovic dragged a shot wide after a driving run from Lucas Moura but Barca began to make better use of its possession, with Alexis Sanchez's shot deflected wide before Messi opened the scoring eight minutes before half-time.
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.
He was replaced by Cesc Fabregas upon the restart, and a Barca statement released during the second half confirmed he will undergo tests on Wednesday to determine the extent of his injury.
Matuidi, impressive defensively in the first half, showed up in attack but was blocked off by Javier Mascherano as he pursued his own heavy touch into the penalty area, though no foul was given. Pique then prevented the all-action Matuidi from reaching Ibrahimovic's pass.
The imperious Thiago Silva's clearance denied Barca a second goal and Sanchez could not connect properly with Fabregas' deep cross, shooting weakly at Salvatore Sirigu.
Matuidi was booked for fouling Iniesta, ruling him out of the return leg, before Lavezzi was replaced by Jeremy Menez.
Alves went close to a goal of his own when he curled a free-kick just wide before Mascherano chopped down Menez to also earn himself a ban.
Menez's free-kick 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.
Substitute Kevin Gameiro was almost sent through by Ibrahimovic's flick-on, only for the bounce to deceive the diminutive France international.
With a minute remaining, though, a penalty handed Barca the advantage in the tie once more.
Sirigu was booked for pulling down Sanchez and Xavi sent the goalkeeper the wrong way from the spot.
Ibrahimovic lashed another effort into Valdes' net but this time was correctly flagged offside - 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.