The hosts looked destined for a point against the Verts after a second-half equaliser cancelled out their early goal, but the striker bagged all three points with his strike
Yannick Ferreira-Carrasco opened the scoring early in the game from inside the 18-yard box but the Rouge et Blanc were pegged back four minutes into the second half when Romain Hamouma equalised for the Verts.
Claudio Ranieri's men were struggling to fashion chances for an equaliser but late arrival Ocampos slotted in a James Rodriguez cross at the far post to seal all three points in the table-toppers' favour.
The hosts started the stronger, with Rodriguez, Ferreira-Carasco and Radamel Falcao taking the game to Saint-Etienne. An awful back-pass from Renaud Cohade rolled straight to the feet of Rodriguez who was denied by a super save from goalkeeper Stephane Ruffier.
But, in the 11th minute, Christopher Galtier's men were behind when Rodriguez threads through-ball behind the back four of the visitors and Belgian attacker Ferreira-Carasco finishes when one-on-one with Ruffier.
Monaco allowed their opposition space to work their way back into the game but remained the more dominant side as the half drew to a close, despite Franck Tabanou and Romain Hamouma testing the hosts' defence.
After half-time, though, the Rouge et Blanc were unable to keep a clean sheet any longer. Cohade played a fine pass inside the box after Faouzi Ghoulam's graft to Hamouma, who deftly equalised for the visitors.
The game became more even after the goal and either side could have been considered potential victors, though the final 20 minutes saw a surge in chances for Monaco.
Defeat for Ranieri's men would have guaranteed surrendering the top spot in Ligue 1 to either Olympique de Marseille or Paris Saint-Germain this weekend and they pressed hard for all three points late on, with Ferreira-Carasco, Falcao and Joao Moutinho causing problems for Saint-Etienne.
But it was substitute Ocampos, who came on with eight minutes to go, who made the difference for the principality club, notching in from six yards with fewer than four minutes to goat the Stade Louis II.
The win means that Monaco go top of the Ligue 1 table, but PSG can displace them with a three-goal-or-more victory over Marseille in Sunday's Classique.