Eden Hazard's penalty had given the London club a potentially vital away goal, but Javier Pastore's brilliant stoppage-time solo goal, added to earlier strikes from Ezequiel Lavezzi and a David Luiz own goal, helped PSG to a two-goal advantage heading into next week's second leg at Stamford Bridge.
Chelsea, the 2012 winners, were looking to book their place in a seventh semi-final in 11 campaigns but started without a recognised striker. With Samuel Eto'o injured, Jose Mourinho selected Andre Schurrle as a 'false nine', appearing to finally lose patience with Fernando Torres.
PSG, unbeaten in their previous 28 European home games, began with a bang and took a fourth-minute lead when one of the three strikers Mourinho had highlighted struck a fine half-volley. It was Lavezzi, rather than Zlatan Ibrahimovic or Edinson Cavani, who fired into the roof of the net after a poor headed clearance from John Terry.
Chelsea equalised before the interval when Hazard, courted by PSG, converted a penalty after Oscar was fouled by Thiago Silva. Hazard also hit the post before half-time and the French side were denied a spot-kick when Cavani tumbled under Gary Cahill's aerial challenge.
Torres replaced Schurrle after 60 minutes, but no sooner had he joined the action than Chelsea were behind again as Lavezzi's free-kick was bundled into the net by David Luiz.
Ibrahimovic departed clutching his right hamstring with more than 20 minutes remaining and will miss the return leg, but Pastore ensured the night and perhaps the tie would end in PSG's favour, beating Petr Cech at his near post after a mazy run.
Cahill later admitted Chelsea face a tough task to reach the semi-finals after conceding that "horrible" late goal. "It's a sloppy goal and unlike us. It's a big blow at 2-1," said the defender.
Mourinho was more scathing in his assessment of the defending. "He [Cahill] says sloppy. I say ridiculous," said the manager.
"We played against a great team, full of good players, especially attacking players. You would expect them to score fantastic goals. Not the goals they scored. We lose the first goal in an easy position and we assist the striker.
"Nobody in the second goal was there for a crucial position. The second goal one of my players scores an own goal, it's unlucky, but the way the team positioned themselves defensively was not the right one.Finally, the third goal was sloppy, Gary uses that word, but for me, ridiculous."
Mourinho appeared disappointed with striker Torres too, after he came on after an hour for Schurrle, who had been fairly ineffective in an unaccustomed lone striker's role. But Mourinho was not willing to defend his initial formation.
"Don't ask me about that," he said. "I change with 1-1 because I thought Fernando could give us more depth than Andre. With Andre the team had good control and possession, he was dropping deep. I thought Fernando could give us a bit more."
Mourinho has lamented his striking options all season - Samuel Eto'o was unavailable through injury - and suggested Chelsea's lack of firepower made hope of recovering the tie a tough prospect.
"It is a difficult job but not impossible," he said. "They [PSG] are the type of team that out of nothing they can score goal.
"We are not a team full of talent to score goals, especially at this level. But you never know. We have to try. We have to go with everything. Let's try."