Eden Hazard's penalty had given the Blues 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, saw PSG take a two-goal advantage into next week's second leg at Stamford Bridge.
Chelsea, the 2012 European champions, 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 could be the difference in the contest 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 PSG were denied a spot-kick when Cavani turmbled 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 swung in menacingly and bundled into the net by David Luiz.
Ibrahimovic, still chasing a first Champions League triumph, departed clutching his right hamstring with more than 20 minutes remaining - but Pastore ensured the night and potentially the tie would end in PSG's favour, beating Petr Cech at his near post after a mazy run.
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