Former Chelsea defender Alex headed home on 61 minutes, two minutes after Andre Ayew had cancelled out Jeremy Menez's early opener to put PSG on 63 points with seven games left.
They are second to Montpellier on goal difference but the leaders have a game in hand, which they will play at Marseille's Stade Velodrome on Wednesday.
PSG's display was passable at best, but it was enough to see off Marseille who, despite some good spells at the Parc des Princes, continued their poor run with a 10th defeat in their last 11 games in all competitions. They remained ninth on 40 points.
"It's always a special game, I think we had a bigger desire to win," PSG keeper Salvatore Sirigu told Canal +.
"The best thing, however, is that we stay in contact with Montpellier."
Marseille levelled just before the hour when Andre Ayew headed home after being set up in the box by Loic Remy's header, but they could not stay focussed and conceded from the restart.
Alex beat Alou Diarra in the air to head home a corner-kick and restore PSG's advantage.
"We were strong, we played well. We were the strongest team," a dejected Jordan Ayew said.
"But we need to move on and go past this huge disappointment."
