Emmanuel Riviere's second-half strike put the principality side on 69 points from 33 games, 10 adrift of champions PSG, who travel to Olympique Lyon on Sunday.
A Monaco defeat would have given PSG the opportunity to clinch their second title in a row with five games to spare, but Claudio Ranieri's side, who are set to secure a direct Champions League qualifying spot, decided otherwise.
Visitors Monaco were the first in action with Joao Moutinho's early drive going just over the bar and Riviere's low shot being blocked by Benoit Costil.
Layvin Kurzawa also came close from close range midway through the first half but Costil made another good save.
Kurzawa left the pitch with a thigh injury shortly before the break and was substituted by Andrea Raggi.
Monaco went ahead 10 minutes into the second half when Riviere beat Costil from close range after being set up by Jeremy Toulalan.
Rennes pushed hard to equalise but the Monaco defence, perfectly marshalled by Ricardo Carvalho, held on.
Monaco, however, were without French international defender Eric Abidal, whose chances of making it into France's World Cup squad look extremely slim as he was not included in the squad.
Ligue Un results
Lille 1 - 0 Valenciennes
Ajaccio 1 - 1 Bordeaux
Evian Thonon Gaillard 2 - 1 Bastia
Nice 1 - 2 Lorient
Rennes 0 - 1 Monaco
Sochaux 2 - 0 Toulouse
- Sports & Recreation
- Emmanuel Riviere