Ezequiel Lavezzi opened the scoring for Laurent Blanc's hosts on four minutes with a sweetly-struck half-volley, but Eden Hazard kept his cool from the penalty spot on 27 to draw Jose Mourinho's men level.
Hazard hit the upright in a lively first half for the Belgian playmaker - but the Parisians gained a first-leg lead to take to London next Tuesday when David Luiz turned a free-kick from Lavezzi into his own net just after the hour mark.
The visitors tried to ensure PSG only had a one-goal advantage as they defended deep in the closing stages - but a magical run from Javier Pastore in stoppage-time saw him jink past three Chelsea defenders before steering a low drive past Petr Cech at his near post to make it 3-1 on the night.
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, Mourinho selected Andre Schurrle as a 'false nine', appearing to finally lose patience with Fernando Torres.
The Germany international performed the same role against Manchester United last August in a dour goalless draw and Mourinho would have been content for a similar result.
That possibility was soon extinguished as Ibrahimovic robbed Luiz and Terry's weak header from Blaise Matuidi's cross fell for Lavezzi, who hit an exquisite half-volley into the roof of Cech's net.
Chelsea were struggling to get hold of the ball, giving it away freely, and a poor Schurrle corner resulted in a Lavezzi-led counter-attack and Ramires halting the move cynically at halfway.
The Brazil midfielder, in the middle of a domestic suspension, will miss next Tuesday's second leg as a result.
PSG were content for Chelsea to pass the ball at the back and - bar one Luiz shot from distance which was easily held by Salvatore Sirigu - there was little danger from the visitors.
The threat from PSG was all the more apparent, as Lavezzi held off Cahill to squeeze a shot into the side-netting.
Chelsea were awarded a penalty when Thiago Silva mis-timed his lunge towards Oscar, felling his compatriot. Hazard sent Salvatore Sirigu the wrong way from the spot to equalise.
The Belgium forward then beat Sirigu again only to strike the foot of the post with a fine volley.
PSG were denied after Ibrahimovic beat Terry to a cross from the right and nodded centrally towards Cavani, who hit the deck as he battled with Cahill.
On this occasion Serbian referee Milorad Mazic was unmoved.
PSG had slackened off after the opening goal and resumed after the break with renewed vigour, Lavezzi rising unopposed to head just over from Matuidi's left-wing cross.
With PSG pushing for a second, Mourinho realised Chelsea would have space on the break and replaced Schurrle with Torres with 30 minutes remaining.
Moments after Torres entered the fray the hosts had their second when Lavezzi's wickedly inswinging free-kick bamboozled everybody, particularly Luiz, who inadvertently kicked the ball into his own net.
Hazard made a fine burst as he tried to spark Chelsea, but Thiago Silva cut out his pass intended for Torres.
Willian then beat Maxwell on the Chelsea right, but no-one was in the box to react to his cross.
Ibrahimovic, after a subdued performance, limped off, with Cavani moving into a central role.
The Uruguay striker wrong-footed the entire Chelsea defence with six minutes to go and his fierce shot beat Cech but went past the post.
PSG claimed their third when Pastore danced around three Chelsea defenders on the right of the box, cut in and beat Cech with a fine shot.