Claudio Ranieri's side jumped back ahead of Lille after they overcame a gutsy visiting defence at Stade Louis II
Claudio Ranieri's moved to within two points of league leaders Paris Saint-Germain as Emmanuel Riviere grabbed the only goal of the game, connecting with Andrea Raggi's cut-back to smash home from close range in the second half.
The hosts had a number of chances early on but the heroics of Ajaccio keeper Francisco Guillermo Ochoa ensured the game remained goalless as he denied Jeremy Toulalan and Riviere.
Ricardo Carvalho was then thwarted in the second period as he rose to meet Joao Moutinho's corner as it began to look as though the visitors could get something out of the game.
Ajaccio's job of keeping their opponents at bay got even tougher after captain Jean-Baptiste Pierazzi was sent off for a second bookable offence and, with the extra man advantage, les Rouge et Blanc finally made their pressure count when Riviere finished from inside the six-yard box.
James Rodriguez almost doubled the home side's advantage late on but his free kick struck the post as Monaco were made to settle for a slender - but crucial - victory.