Leonardo Jardim's side bounced back from defeats to PSG and Nice by beating Angers and Troyes earlier this month, and have now made it three straight Ligue 1 victories to close the gap on the leaders.
Saint-Etienne, however, are now without a victory in the league since the middle of October, with the result leaving them in 15th position in the table - just two points outside of the bottom three.
It took just three minutes for Monaco to make the breakthrough on the night, with full-back Djibril Sidibe finding the top corner from the edge of the box.
It got worse for Saint-Etienne when Stephane Ruffier was shown a straight red card after the goalkeeper disputed Monaco's third amid calls for offside.
The goal stood as Ruffier saw red for his conduct towards the linesman on the near side, and Monaco then made it four on the hour through Keita to cap a miserable night for the hosts.
PSG will have the chance to again move nine points clear of the reigning champions when they travel to Rennes on Saturday afternoon.