A costly error by Chelsea goalkeeper Filip Jorgensen sparked a late collapse as Khvicha Kvaratskhelia's double gave Champions League holders Paris St?Germain a three?goal lead going into next week's last-16 second leg.
Chelsea had played well, bringing the score back to 2?2, but Jorgensen's pass straight to PSG's Bradley Barcola before being lobbed by Vitinha let the European champions restore their lead for the third time at Parc des Princes.
However, substitute Kvaratskhelia curled a wonderful strike from the edge of the box before giving Chelsea a mountain to climb by making it 5-2 with a sidefooted finish with virtually last kick of the match.
It could have been a much better night for Chelsea, who performed well for 75 minutes, despite going a goal down inside 10 minutes.
Barcola opened the scoring with a powerful shot through several Chelsea bodies and inside the near post after Ousmane Dembele's cross was nodded into his path.
Jorgensen then tipped Dembele's powerful effort on to the post, but Malo Gusto equalised for Chelsea, shooting past the unconvincing goalkeeper Matvei Safonov after his run was picked out by Enzo Fernandez.
Just 14 seconds after Cole Palmer struck a shot straight at Safonov from inside the penalty area, Dembele was celebrating putting PSG back in front.
He outran Chelsea defender Wesley Fofana and found the space for a composed sidefoot finish. It was Desire Doue's creativity that allowed him to evade challenges from Moises Caicedo and Trevoh Chalobah in midfield before playing in last year's Ballon d'Or winner.
However, Doue would cost PSG in the second half when he was caught in possession by Neto, whose low cross was steered into the net by the onrushing Fernandez to level the match again for Chelsea.
Less than five minutes later, PSG manager Luis Enrique replaced Doue with exciting Georgia attacker Kvaratskhelia.
It was Jorgensen's costly error - a misplaced pass straight to Barcola - that allowed Vitinha to lob the out?of?position goalkeeper and restore the Parisians' lead for the third time on the night.
A cruel moment for Chelsea was followed by one of pure magic as Kvaratskhelia delivered an unstoppable curling strike from the edge of the box, with a further sidefoot finish making it five goals for the European champions.
Chelsea will now have to overturn a three?goal deficit when they host PSG in the second leg at Stamford Bridge on Tuesday night.
It is remarkable to think PSG went into this tie under pressure domestically after defeat at Monaco and an unconvincing start to 2026.
This team, lauded as the best in Europe last season, have been far less convincing and only reached this stage through the play?off round - a tie they almost threw away despite facing 10?man Monaco in both legs.
Even in the pre?match media conferences, there were frosty exchanges between local reporters and manager Luis Enrique, while Barcola was asked why he had not scored a Champions League goal for more than a year.
He answered that question on the pitch, powering in a volley through a crowd of players and past the goalkeeper after just 10 minutes.
It was a sensational performance from the pacey attacker, selected ahead of Kvaratskhelia, and came on a night when Dembele was also under scrutiny for not matching last season's level.
Once again showing why he is considered the best player in the world, the Frenchman put PSG back in front after Gusto had punished poor marking at the back to level.
Dembele's goal had been created brilliantly by Doue, but it was the winger who cost his side for Fernandez's equaliser by misjudging the flight of the ball and then failing to prevent Neto's delivery.
Such are the riches at Luis Enrique's disposal that he could call on Kvaratskhelia, who delivered emphatically late in the match.
Chelsea had been every bit as creative in midfield, energetic, and bold tactically.
But they were ultimately outgunned by Europe's most thrilling attack.
It was high risk and no reward for Chelsea on Wednesday night.
They had gone toe?to?toe with the best team in Europe on their own turf for 74 minutes, but after Jorgensen's mistake, that positive display unravelled into a whimpering collapse.
A lack of concentration, ill?discipline and, perhaps, a shortage of real quality at the highest level left Chelsea well beaten.
When it came to concentration, Jorgensen was the prime culprit. Playing in arguably the biggest game of his career in the last 16 of the Champions League, he threw away his opportunity to stay as number one ahead of Robert Sanchez.
It could well be that neither goalkeeper is good enough, with Sanchez having struggled in two of recently appointed head coach Liam Rosenior's first three games against Arsenal, which ultimately got him dropped.
But Jorgensen was far from the only one at fault. One of the star performers this season, captain Reece James, stumbled when challenged by Senny Mayulu for the fourth goal, while Chelsea were simply played through, leaving several players out of position for the fifth.
Even Palmer squandered a crucial chance 14 seconds before Dembele scored a more difficult one on the counter?attack.
And, to highlight Chelsea's indiscipline, Neto pushed over a ball boy after the fourth goal, sparking a mass altercation between both sides.
The Portugal winger attempted to repair the damage after the match by giving the ball boy his shirt, but he risks facing further Uefa action.
It was another damning indictment of a team that can be brilliant at their best but implode at their worst.
It came against PSG, one of the few teams younger than Chelsea in Europe's top?tier competition, showing that success is possible with a youthful squad.
However, PSG proved on the night they have cooler heads, greater quality and are everything Chelsea want to be but are struggling to become.
Reece James and Trevoh Chalobah react after conceding Chelsea's fifth goal in Paris
Chelsea host Newcastle United in the Premier League on Saturday, 14 March (17:30 GMT), before the return leg against PSG at Stamford Bridge on Tuesday, 17 March (20:00).
PSG have a week off before the second leg in west London after they had a request to postpone a Ligue 1 match granted.