Ten-man Monaco struck twice late on to leave Chelsea's Champions League hopes hanging in the balance.
Hernan Crespo's close range strike gave Chelsea a crucial away goal when he swiftly levelled Dado Prso's header after 15 minutes in the semi-final.
But after Andreas Zikos was sent off following a second-half clash with Claude Makelele, Chelsea collapsed.
Fernando Morientes fired home after 78 minutes, then substitute Shabani Nonda added a third four minutes later.
And Chelsea manager Claudio Ranieri must take much of the blame, turning the course of the match Monaco's way with a series of inexplicable substitutions.
Monaco crowned an impressive opening spell with a deserved opener after 15 minutes.
Mario Melchiot was booked for a wild tackle on Jerome Rothen - and it proved an expensive challenge.
Rothen's free-kick evaded the diving Crespo and Prso took advantage of a favourable bounce to direct a powerful header past Marco Ambrosio into the top corner.
Chelsea needed an instant response, and Crespo provided it with the crucial away goal six minutes later.
Scott Parker set up Eidur Gudjohnsen, who slipped but managed to find the lurking Crespo, who turned and scored from eight yards.
15 mins: Dado Prso heads Monaco in front
21 mins: Hernan Crespo equalises for Chelsea
52 mins: Andreas Zikos sent off after clashing with Claude Makelele
78 mins: Fernando Morientes puts Monaco back in front
82 mins: Substitute Shabani Nonda adds a third
It was the signal for a transformed Chelsea display, with the show being controlled by a majestic first-half performance from Frank Lampard.
The midfielder fired a long-range drive narrowly wide, then delivered a dangerous cross which the stretching Crespo diverted over the bar.
Ranieri made an interval change, removing Jesper Gronkjaer for Juan Sebastian Veron.
The move handed the initiative back to Monaco, who almost regained their lead in a hectic opening to the second half.
Ambrosio saved brilliantly from Prso after 50 minutes, and seconds later Marcel Desailly cleared Fernando Morientes' bicycle kick off the line.
Monaco were then reduced to ten men after Zikos was shown the red card.
Makelele raised a hand to the Greek, and when he responded the Chelsea midfield man collapsed to the floor in shamefully melodramatic fashion.
As Zikos walked off, Makelele was booked, which will keep him out of the second leg at Stamford Bridge.
Chelsea almost took advantage of their numerical advantage, with Gudjohnsen heading just wide, and Monaco goalkeeper Flavio Roma denying Melchiot in a desperate goalmouth scramble.
Ranieri then made two more unpredictable changes, replacing Melchiot with Jimmy Floyd Hasselbaink, then removing Parker for Robert Huth.
Chelsea were suddenly unbalanced, and resurgent Monaco were in front after 78 minutes when Morientes thrashed a stunning finish past Ambrosio.
The goalkeeper was then badly at fault four minutes later, letting a tame effort from substitute Nonda, with his first touch, through his hands for the third.
Monaco: Roma, Evra, Ibarra, Bernardi, Giuly (Nonda 83),
Prso (Cisse 57), Morientes, Zikos, Rothen (Plasil 89),
Subs Not Used: Sylva, Oshadogan, Adebayor, El Fakiri.
Sent Off: Zikos (53).
Chelsea: Ambrosio, Makelele, Desailly, Lampard,
Melchiot (Hasselbaink 62), Bridge, Parker (Huth 69), Crespo,
Gudjohnsen, Terry, Gronkjaer (Veron 46).
Subs Not Used: Sullivan, Mutu, Cole, Geremi.
Booked: Melchiot, Makelele, Terry.
Referee: Urs Meier (Switzerland).