The Belgium defender struck the winner two minutes into added time to put PSG on 25 points from nine games and they lead champions Monaco, who lost 3-2 at Olympique Lyonnais on Friday, by six points.
Dijon's Benjamin Jeannot scored three minutes from time to cancel out Meunier's second-half opener but the full back grabbed his second to earn PSG three points after their attacking players had failed to shine.
With Edinson Cavani rested on his comeback from international duty with Uruguay and Marco Verratti, Layvin Kurzawa and Thiago Silva injured, PSG were without four regular starters.
Their absence was felt as they struggled to create chances in the first half against a resolute Dijon defence.
Neymar was often beaten to the ball by alert Dijon defenders and French striker Kylian Mbappe was barely seen.
PSG, however, had the best chance on the stroke of halftime when Dani Alves's free kick crashed against the bar.
PSG went ahead after 70 minutes when Meunier poked the ball home after Julian Draxler's shot was parried away into his path by Baptiste Reynet.
Jeannot levelled with a fine 30-metre volley, only for Meunier to snatch victory for PSG with a shot from inside the box.
(Reporting by Julien Pretot, editing by Ed Osmond)
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