Courbis returned for a second stint in charge of the 2011-12 Ligue 1 champions earlier this week following the resignation of Jean Fernandez.
But the 60-year-old could not inspire the struggling hosts to victory, Montpellier succumbing to a defeat that extends their winless run to nine games.
Saint-Etienne dictated for much of the first half, with winger Franck Tabanou going close to giving them the lead on multiple occasions.
Christophe Galtier's men finally broke down the home defence in the 75th minute when former Leeds United forward Max Gradel turned home Faouzi Ghoulam's low cross at the far post.
Montpellier failed to mount a response, allowing Saint-Etienne to hold on and claim their third league win in four games.
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