Angers came into the weekend as the nearest challengers to runaway leaders Paris Saint-Germain but dropped 10 points adrift as Mario Pasalic's first-half goal at the Stade Louis II snapped the visitors' six-game unbeaten run.
For Monaco it was the first time they had registered back-to-back wins this campaign as Leonardo Jardim's side moved up three places to sixth, two points behind second-placed Lyon, who are above Angers and Saint-Etienne on goal difference.
Angers have made an incredible start to their first season back in the French top flight since 1994 but were undone by Chelsea loanee Pasalic's close-range finish on 35 minutes after a knockdown header from towering Ivorian striker Lacina Traore.
Stephan El Shaarawy came close to adding a second just after half-time but the toe of Ismael Traore diverted the Italy international's shot just wide of Ludovic Butelle's near post.
Rony Lopes then produced a glaring miss shortly after when he somehow failed to hit the target after Elderson Echiejile's low cross had seemingly presented the Portuguese midfielder with a simple tap-in.
Skipper Cheikh N'Doye had the best chance to snatch a point for Angers but the Senegalese midfielder nodded wide from Abdoul Camara's looping cross in the closing stages.
Earlier, Nice were held in check by Lille in a 0-0 draw at the Allianz Riviera while Marseille, just three points above the relegation zone, visit Nantes later on.
Reigning champions Paris stretched their already sizeable lead at the top with a 1-0 victory in Rennes on Friday courtesy of Angel di Maria's second-half strike.
Lyon climbed up to second on Saturday as Claudio Beauvue's late penalty steered them to an unconvincing 1-0 win over 10-man Troyes, with Saint-Etienne easing to a 3-0 win over a slumping Reims side.