The victory on Saturday put Monaco on 16 points from seven games, two points ahead of Nice who travel to Nancy on Sunday. Angers are 12th with nine points, reports Xinhua.
The Principality side, who were thrashed by Nice three days ago, trailed Angers just 11 minutes into the second half after Famara Diedhiou latched onto a cross by Toko Ekambi.
Monaco hit back in the 66th minute when Kamil Glick volleyed home from a bad clearance by the visitors' defence.
Dickson Nwakaeme, however, turned the ball into his own net in the 75th, some five minutes after he had replaced Diedhiou.
Paris St Germain, who suffered their second defeat of the season on Friday, losing 2-0 at Toulouse, now trail Monaco by three points.
In other matches, Bastia nipped a 1-0 home win over Guingamp to go up to the ninth, Bordeaux were held goalless with Caen, Dijon claimed their second victory of the season, 3-0 over Rennes, and Motpellier suffered at home, losing 1-0 to Metz.
