The visitors took the lead in the seventh minute when Carlos Eduardo curled a free kick from just outside the box into the bottom corner.
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Moutinho and Yannick Ferreira-Carrasco then saw efforts blocked towards the end of the first half as they went into the break trailing.
In the second half Eduardo and Dimitar Berbatov both headed over as Monaco pushed for a way back into the match.
Despite their dominance the hosts were unable to find the net and they slipped to their fourth defeat from eight league games.