A fine display from Ezequiel Lavezzi was the catalyst for a confident performance from the hosts, with Eden Hazard's first-half penalty providing a glimmer of hope for the Blues
The French champions showed the full array of attacking flair that has put them on the verge of defending their Ligue 1 crown this term to claim a healthy advantage, leaving Chelsea with plenty to do in the return clash at Stamford Bridge next week.
Ezequiel Lavezzi - a constant menace to the Londoners' defense - put the hosts ahead inside the opening four minutes of the encounter at the Parc des Princes with an effort from 12 yards.
But Chelsea was back on level terms shortly before the half-hour mark when Eden Hazard converted from the penalty spot after Thiago Silva had carelessly felled Oscar in the box.
Hazard then hit the post before the end of the first half as Chelsea pushed for the lead, but David Luiz found his own net - after giving away a cheap free kick - to restore PSG's lead.
PSG talisman Zlatan Ibrahimovic was worryingly withdrawn in the second half, appearing to be nursing a hamstring injury.
But the French side soon forgot about that blow when substitute Javier Pastore - a late replacement for Lavezzi - added a superb third in injury time to give his side a two-goal margin.
Chelsea opted to start without a recognized striker, leaving Fernando Torres and Demba Ba on the bench, while PSG boasted one of the most recognizable of them all in Ibrahimovic, who this week appeared to rule out a future move to the Premier League.
While Jose Mourinho's men will have been suitably prepared to deal with the Swedish frontman's capabilities, it was Lavezzi who struck the first blow four minutes in.
The Argentine superbly controlled a weak headed clearance from John Terry on his chest, before allowing the ball to bounce and firing a left-footed effort into the top corner of the net from the center of the penalty area.
Lavezzi continued to pose a threat to the Chelsea goal, sending an attempt into the side netting after 25 minutes, but a clumsy challenge on Oscar by masked captain Thiago Silva – recovering from a fractured cheekbone – offered the Premier League outfit a way back into the clash just two minutes later.
Referee Milorad Mazic pointed to the spot and Hazard made no mistake in rolling the ball beyond Salvatore Sirigu, who leapt the wrong way.
Hazard – back in the country where he cut his teeth as a player with Lille – almost doubled his tally five minutes before the break, striking the right-hand post with a volley from a chipped Willian cross.
As in the first half, PSG started brightly once again after the interval, Lavezzi heading narrowly over from a Blaise Matuidi cross when unmarked in the box.
And the French side was back in front just after the hour, when Luiz inadvertently knocked the ball into his own net from a teasing Lavezzi free kick.
However, there were worrying scenes for the hosts in the 68th minute, when Ibrahimovic, who was quiet for much of the encounter, pulled up with what appeared to be a hamstring strain.
Cavani's late curling effort whistled just wide of the right-hand upright, but Pastore forced his way into the penalty area in stoppage time to drive home from a tight angle and compound Chelsea’s misery.