Lorient opened the scoring through Vincent Aboubakar's ninth minute penalty and although Radamel Falcao hit back with a spot kick of his own on 78 minutes, Valentin Lavigne grabbed the winner three minutes from time.
Monaco also had defender Ricardo Carvalho sent off in the 67th minute for a second yellow card.
The principality club, who under Russian billionaire Dmitry Rybolovlev splashed out more than 100 million euros (79 million pounds) on transfers last year, finished last season nine points adrift of Paris St Germain but still qualified automatically for this term's Champions League.
Despite their bank balance and relative success in their first campaign back in the top flight, Monaco sold World Cup top scorer Rodriguez to Real Madrid in the close season and fellow Colombian Falcao is constantly linked in the media with a move.
Portuguese Leonardo Jardim was appointed as Monaco coach in June after the club replaced Italian Claudio Ranieri in a bid for a "new dynamic".
Olympique Lyonnais won 2-0 at home to Stade Rennes in their season opener, midfielder Steed Malbranque putting them ahead in the 64th minute and Alexandre Lacazette adding a penalty.
Big-spending champions PSG drew their first league match of the new campaign on Friday when they were held 2-2 at Stade de Reims with Zlatan Ibrahimovic scoring twice but missing a penalty.
(Reporting by Maya Nikolaeva, editing by Mark Meadows)
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