Thauvin found the back of the net with a low shot across goal after being set up by Steven Fletcher to send OM, whose coach Michel was sacked on Tuesday, into the final against bitter rivals Paris St Germain on May 21 at the Stade de France.
PSG, who are bidding to replicate last season's domestic treble and take on Lille in Saturday's League Cup final, reached the French Cup final with a 1-0 win at Lorient on Tuesday.
Marseille, with former assistant coach Franck Passi now at the helm, are without a Ligue 1 win in their last 10 games and lie 15th in the table with four games left.
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(This version of the story has been refiled to remove reference to 'League Cup' in headline)
(Reporting by Julien Pretot; Editing by Toby Davis)
