The hosts took the lead early on through Ezequiel Lavezzi, but Chelsea fought back and were level before the half-hour mark as Eden Hazard converted from the spot after Thiago Silva had brought down Oscar.
PSG regained their lead in the 61st minute when David Luiz inadvertently turned Lavezzi's free kick into his own net, while the potentially fatal blow came deep into stoppage time when Javier Pastore danced his way into the box before beating Petr Cech at his near post.
Here, Sports Mole takes an in-depth look at a thrilling 90 minutes of football in the French capital.
On target: 3
On target: 2
Was the result fair?
Yes. A 2-1 scoreline probably would have been a fairer reflection on the match rather than a 3-1 success for the hosts, but there is little doubt that they deserved to win tonight. They made a blistering start to the game, but failed to build upon that as Chelsea settled well and eventually got their equaliser.
However, while the first half was an even affair, PSG had the better of the second half, creating more chances than the visitors. Apart from the goal, Chelsea only really had one other chance - when Hazard hit the post with a volley - while PSG had a few decent openings.
The third goal will be really gutting for Chelsea to concede as they weren't too far off the pace during the match. A momentary lapse in concentration right at the end of the game could end up costing them dearly, with PSG's two-goal advantage looking a lot more comfortable than a 2-1 lead would have done.
They could not have wished for a better start, taking the lead within three minutes, but they will be very disappointed with their failure to build on such a promising beginning to the match. They allowed Chelsea to get back into the game and were duly punished when the visitors got their equaliser.
The pressure on the defence had been slowly mounting without Chelsea really threatening to break through until Thiago Silva's rash challenge conceded the penalty. They failed to react to the visitors' goal and were perhaps lucky to go into the break all square after Hazard hit the post.
However, they were better in the second half and, while not at their free-flowing best, they seemed to have a degree of control over the match. They certainly looked most like scoring, although there also seemed to be a mistake waiting to happen at times.
A similar performance in the second leg may just be enough to see them through with their two-goal advantage, but it is unlikely to take them much further in the competition.
Jose Mourinho would have been looking for a response to the defeat to Crystal Palace on Saturday, but instead he saw his side concede within three minutes. John Terry, who scored the own goal at Selhurst Park, was at fault for the opener when he failed to get enough on his clearance to get it beyond Lavezzi.
However, the visitors responded well and got themselves back into the match. They didn't threaten much before their opening goal but, on the balance of play, deserved to be level at half time. Indeed, had Hazard's volley crept just inside the post rather than hitting the upright, then things may have been a lot different.
The second goal was unfortunate as the defence struggled to deal with a fabulous Lavezzi ball into the box, and David Luiz simply could not get out of the way of it in time. However, the third was just poor defending as Pastore waltzed past some lacklustre tackling and fired past Cech at his near post.
Chelsea would have been content with a 2-1 defeat, safe in the knowledge that Stamford Bridge is a tough place to go. However, that third goal is a killer for the Blues and Mourinho will be livid that it came as a result of poor defending. They will need to be more attacking in the second leg, and Mourinho is highly unlikely to name a starting XI without a recognised striker as he did for tonight's match.
Sports Mole's man of the match
Ezequiel Lavezzi: It was always likely that at least one of PSG's attacking trio was going to have a big impact on tonight's match, and it was Ezequiel Lavezzi who stepped up to the plate. He was a livewire throughout and always looked like PSG's most dangerous player.
His finish for the first goal was superb, showing exquisite technique to volley the ball past a helpless Cech. He kept offering a threat throughout the game and it was his cross that led to the second goal as well. He put the free kick into an area of the box that is nigh-on impossible to defend against, and there was nothing Luiz could have done to prevent it going in off him.
Each goal had its own mistake attached to it, be it Terry's poor clearance for the first, Silva's lunge for the penalty or Luiz's cheap free kick and subsequent own goal. However, the biggest error of the lot could prove to be the defending for PSG's third goal.
Pastore danced past two challenges far too easily to get into a shooting position inside the box, but even then Cech should not have been beaten at his near post. It was poor goalkeeping from a man with such experience, gifting the hosts what could prove to be the decisive goal in the tie.
Milorad Mazic had a good game tonight, keeping control of the match and making sensible decisions. The yellow card only came out when warranted, and he didn't let the raucous atmosphere get to him.
His biggest decision was to award Chelsea a penalty, but he had little choice. It was a clear spot kick as Silva mistimed his sliding challenge on Oscar, and the referee was right to award it.
PSG: PSG will look to make it 11 wins on the trot and move one step closer to an inevitable league title when they host Reims on Saturday.
Chelsea: Chelsea, meanwhile, will host Stoke City at Stamford Bridge as they look to keep their fading title hopes alive.