Lorient made the most of opening the fixtures on the second weekend of the season by jumping to the top of the table with four points.
Monaco, who finished third last season to earn a chance of a place Champions League, left a number of senior players on the bench ahead of their Champions League qualifying playoff first leg against Shakhtar Donetsk on Tuesday.
Moffi was brought down by Monaco summer signing Ismail Jakobs after 31 minutes and took the penalty to score. Moffi was Lorient's top scorer last season with 14 goals, three of them against Monaco.
Monaco dominated possession but struggled to create clear chances. The few strikes on target they managed were blocked by the in-form goalkeeper Paul Nardi.
In front of more than 12,000 spectators, delighted to be back at the Moustoir stadium after almost a season behind closed doors, and increasingly excited as victory approached, Lorient held on to their small lead.