Despite dominating possession, Etienne struggled to create chances but eventually found a way back into the contest when Monaco full back Fode Ballo-Toure's miss hit clearance found his own goal.
Winger Remy Cabella struck from close range to give the visitors a 2-1 lead before assisting Arnaud Nordin's 80th minute header to put the result beyond doubt.
Substitute Carlos Vinicius pulled one back for Monaco but could not prevent their ninth home defeat of the league season.
Monaco, who are without a league win since March, are now just three points clear of the relegation zone, while St Etienne provisionally move to third spot ahead of Olympique Lyonnais on goal difference.
The top three in Ligue 1 qualify for the Champions League, with the third-placed team starting in the third qualifying round of Europe's elite competition.
(Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)
