Both sides were looking for their first wins of the new Ligue.1 season, and Monaco head coach Niko Kovac is under particular pressure to bring a sense of success to the principality side.
But Lorient coach Christophe Pélissier drilled his side well, and it looked dangerous on the counter as Monaco dominated possession without offering much of a threat on goal.
Monaco's Kevin Volland earned the first big chance of the match, but his low drive was saved by Lorient goalkeeper Paul Nardi just before the half hour.
That missed opportunity hurt as shortly after, Lorient was awarded a penalty when Monaco defender Ismail Jakobs was penalised for tugging on the dangerous Moffi's shirt.
Nigeria International Moffi stepped up himself to fire the Lorient ahead from the spot.
Kovac opted to twist in pursuit of an equaliser and introduced Wissam Ben Yedder, Caio Henrique and Aleksandr Golovin to help turn the tide.
But Lorient held firm, sending Monaco to its first defeat of the season.