Third-placed Marseille wasted the chance to go top of Ligue 1, at least for a few hours, with leaders Lyon playing away at arch-rivals St Etienne later (2000 GMT).
Things went wrong for Marseille after Kabore was dismissed in the 38th minute, earning a second yellow card in fouling Jeremie Aliadiere to concede a penalty.
The former Arsenal forward converted the spot-kick by wrong footing Steve Mandanda.
Lorient doubled their lead three minutes into the second half with Benjamin Corgnet flicking the ball past Mandanda from an Alain Traore cross.
Marseille twice went close to reducing the arrears but Fabien Audard denied Souleymane Diawara and Loic Remy with superb saves.
Kevin Monnet-Pacquet put the game beyond the home side's reach in the 69th minute with a fine low shot from just inside the box.
Lorient moved up to eighth on 24 points.
Earlier on Sunday, sixth-placed Girondins Bordeaux drew 0-0 at Stade Reims.