Liverpool opened their Champions League campaign with a morale-boosting win.
Rafael Benitez's side went ahead through a clever goal - Steven Gerrard and Luis Garcia combining to set up Djibril Cisse, who rifled a shot home.
Garcia went close twice before the interval, first drawing a reaction save from Flavio Roma and then hitting the woodwork with an angled header.
Substitute Milan Baros made the game safe for Liverpool with a wonderful individualistic goal late on.
Didiers Deschamps' outfit were a pale imitation of the side that reached last year's final.
Ludovic Guily and Jerome Rothen have left for new pastures, while Javier Saviola was banned and Ernesto
Chevanton and Shabani Nonda were out injured.
Those absentees led to Monaco adopting a defensive strategy deploying three central defenders - Sebastien Squillaci, Gael Givet and Vassilis Zikos.
And it was a tactic that initially stymied Liverpool as they sought to establish a link to Cisse.
After the interval Deschamps withdrew left-back Patrice Evra and introduced another striker, Souleymane Camara, in a bid to rescue the game.
The switch gave Monaco a better balance, although Deschamps' team laboured to create openings.
The best Monaco effort was an Emmanuel Adebayor header, which Dudek saved at the foot of the post.
Early on, Liverpool's best chance was Garcia's ambitious effort - a shot that mirrored an earlier long-range strike for Monaco from Mohamed
Kallon and which almost caught out Jerzy Dudek.
Gradually Cisse's runs began to trouble Monaco's defensive triumvirate, while Gerrard and Garcia began to strike up the rapport that had been such a feature of Saturday's win over West Brom.
A one-two between those two Liverpool midfielders created Cisse's goal, an exchange of passes ending with Gerrard slipping the ball to the former Auxerre striker, who crashed his shot past Roma.
Soon afterwards Kewell's deft header released Garcia, whose low shot was superbly blocked by Roma.
In first-half stoppage time Gerrard and Garcia again combined to great effect as the Spaniard angled a header against Roma's right-hand upright.
Just before the hour Kewell managed to set free Cisse once more but Roma did well to stand his ground and then divert the Liverpool striker's shot.
With 10 minutes to go Garcia should have made the game safe for Liverpool but the Spaniard crashed his shot wide with just the Monaco goalkeeper to beat.
It was left to Baros to apply the coup de grace as he single-handedly outfoxed the Monaco defence with a jinking run before slipping the ball past the keeper.
Liverpool: Dudek, Josemi, Carragher, Hyypia, Riise, Finnan,
Gerrard, Alonso, Kewell (Warnock 76), Luis Garcia (Biscan 87),
Cisse (Baros 69).
Subs Not Used: Kirkland, Diao, Hamann, Traore.
Goals: Cisse 22, Baros 84.
Monaco: Roma, Givet (El Fakiri 80), Squillaci, Rodriguez,
Anjreas Zikos, Maicon, Perez (Juan 89), Farnerud,
Evra (Camara 45), Kallon, Adebayor.
Subs Not Used: Audard, Modesto, Lacombe, Lescure.
Booked: Anjreas Zikos, Givet.
Ref: Terje Hauge (Norway).
Referee: Terje Hauge (Norway).