Defender Mbia followed up after Sochaux keeper Matthieu Dreyer had failed to block his effort from close range to put Marseille on 65 points from 32 games, five points ahead of second-placed Auxerre.
Marseille, who had had two games in hand, won the first last week with a 3-0 home victory over the same opponents.
"We had two games in hand and took six points from them, which is excellent," Marseille coach Didier Deschamps told reporters after his side moved closer to their first league title since 1992.
"You can talk about the title if you want but there are six matches still to play. What is satisfying tonight is that we suffered but showed we had character to take the points," Deschamps added.
Girondins Bordeaux, meanwhile, further undermined their prospects of retaining the title when they conceded their third Ligue 1 defeat in a row by losing 2-1 at strugglers Le Mans.
Bordeaux, who opened the scoring with a headed goal by Brazilian defender Henrique before watching their hosts strike back with goals from forward Anthony Le Tallec and midfielder Mathieu Dossevi, are in fifth place, nine points off the pace, with a game in hand.
Follow FFT.com on Twitter
Join FFT.com on Facebook
