The principality team have 36 points from 21 games but are still a long way adrift of leaders Paris St Germain who beat Toulouse 1-0 away on Saturday to reach 57 points.
Monaco had to contend with the loss of midfielder Nabil Dirar to a thigh injury after half an hour and managed only one shot on target before the break.
They came out much stronger in the second half and Lemar opened the scoring after collecting a through pass from Moutinho and blasting the ball beyond keeper Benjamin Lecomte.
Moutinho doubled the tally four minutes later with a perfectly curled free kick.
"We played better after the interval, we were better with the ball and more aggressive. Our first idea was to defend well and we also did that," said coach Leonardo Jardim.
St Etienne won France's hottest derby by beating Olympique Lyonnais 1-0 at Geoffroy Guichard with Alexander Soderlund scoring the only goal.
The Norway striker, who joined the club earlier this month, found the net in the 76th minute when he slotted the ball past Anthony Lopes after being set up by Kevin Monnet Pacquet.
St Etienne are fifth on 32 points, three points ahead of ninth-placed Lyon.
Olympique de Marseille are eighth on 29 after a 3-1 win at Caen with goals by Michy Batshuayi, Georges Kevin N'koudou and Bouna Sarr.
(Reporting by Julien Pretot; Editing by Martyn Herman and Ken Ferris)
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