Monaco - who are top on goal difference - can restore their three-point lead if they beat Nantes on Sunday (20:00 GMT).
PSG beat Nancy 1-0 thanks to Edinson Cavani's late penalty, his 37th goal of the season, and they were lucky not to concede when Alexis Busin's shot hit both posts.
Nice won by the same scoreline against Dijon, with Wylan Cyprien scoring in the 69th minute.
Match ends, Paris Saint Germain 1, Nancy 0.
Second Half ends, Paris Saint Germain 1, Nancy 0.
Foul by Edinson Cavani (Paris Saint Germain).
Modou Diagne (Nancy) wins a free kick in the defensive half.
Offside, Paris Saint Germain. Javier Pastore tries a through ball, but Julian Draxler is caught offside.
Layvin Kurzawa (Paris Saint Germain) wins a free kick in the attacking half.
Foul by Benoit Pedretti (Nancy).
Thiago Silva (Paris Saint Germain) wins a free kick in the defensive half.
Foul by Youssouf Hadji (Nancy).
Attempt missed. Youssouf Hadji (Nancy) left footed shot from the right side of the box is close, but misses the top left corner. Assisted by Faitout Maouassa.
Substitution, Nancy. Youssouf Hadji replaces Issiar Dia.
Attempt missed. Hatem Ben Arfa (Paris Saint Germain) left footed shot from the centre of the box misses to the left. Assisted by Edinson Cavani.
Attempt saved. Javier Pastore (Paris Saint Germain) right footed shot from the left side of the box is saved in the centre of the goal. Assisted by Hatem Ben Arfa with a through ball.
Attempt saved. Faitout Maouassa (Nancy) left footed shot from outside the box is saved in the bottom right corner.
Attempt blocked. Faitout Maouassa (Nancy) left footed shot from outside the box is blocked.
Hatem Ben Arfa (Paris Saint Germain) wins a free kick on the right wing.
Foul by Diallo Guidileye (Nancy).
Attempt saved. Edinson Cavani (Paris Saint Germain) header from the right side of the box is saved in the centre of the goal. Assisted by Hatem Ben Arfa with a cross.
Substitution, Nancy. Benoit Pedretti replaces Youssef Ait Bennasser.
Corner,  Paris Saint Germain. Conceded by Vincent Muratori.
Goal!  Paris Saint Germain 1, Nancy 0. Edinson Cavani (Paris Saint Germain) converts the penalty with a right footed shot to the bottom left corner.
Penalty Paris Saint Germain. Serge Aurier draws a foul in the penalty area.
Penalty conceded by Sergei Chernik (Nancy) after a foul in the penalty area.
Corner,  Paris Saint Germain. Conceded by Erick Cabaco.
Delay over. They are ready to continue.
Substitution, Paris Saint Germain. Hatem Ben Arfa replaces Gonçalo Guedes.
Delay in match Youssef Ait Bennasser (Nancy) because of an injury.
Attempt blocked. Alexis Busin (Nancy) right footed shot from the left side of the box is blocked. Assisted by Faitout Maouassa.
Attempt blocked. Thiago Silva (Paris Saint Germain) right footed shot from outside the box is blocked. Assisted by Javier Pastore.
Alexis Busin (Nancy) hits the left post with a right footed shot from the left side of the box. Assisted by Youssef Ait Bennasser following a fast break.
Corner,  Paris Saint Germain. Conceded by Vincent Muratori.
Blaise Matuidi (Paris Saint Germain) wins a free kick on the left wing.
Foul by Joffrey Cuffaut (Nancy).
Corner,  Paris Saint Germain. Conceded by Loic Puyo.
Substitution, Nancy. Alexis Busin replaces Anthony Koura.
Attempt missed. Thiago Silva (Paris Saint Germain) header from the centre of the box is too high. Assisted by Julian Draxler with a cross following a set piece situation.
Javier Pastore (Paris Saint Germain) wins a free kick in the attacking half.
Foul by Diallo Guidileye (Nancy).
Attempt missed. Julian Draxler (Paris Saint Germain) right footed shot from outside the box is high and wide to the right. Assisted by Marco Verratti.
Thiago Silva (Paris Saint Germain) wins a free kick in the defensive half.
Paris St-Germain and Nice both won on Saturday to make it a three-way tie on points at the top of Ligue 1.