Barca host the side from the French capital for the return leg next week with a potentially vital away goal from Jenni Hermoso for the opener after 12 minutes against her former club. This season's top scorer increased her tally to six in a tightly contested match at Saint-Germain-en-Laye.
But what could have been a tricky tie to turn around for PSG suddenly looked more accessible after Alana Cook's 21st-minute leveller. The American was the surprise addition in PSG coach Olivier Echouafni's team and was deployed as a right-back with Canadian Ashley Lawrence moving up into attack to help fill the void left by the injured Kadidiatou Diani.
PSG had knocked out multiple champions Lyon in the quarter-finals but they travel to Spain with their ticket to the May 16 final in Gothenburg far from guaranteed.
Aside from Cook's decisive intervention they also had goalkeeper Christiane Endler to thank for keeping them in the hunt after some fine saves to deal with. These included an early chance from Caroline Graham Hansen, an attempt at a double from Hermoso, and Alexia Putellas' 53rd-minute freekick.
On hand to watch the game was Mauricio Pochettino, whose PSG's men are preparing for their Champions League semi-final against Manchester City on Wednesday. Sunday's second women's quarter-final sees Bayern Munich take on Chelsea.