Gameiro goal helps PSG close in on Montpellier
The win gave PSG 36 points from 17 games, level with Montpellier, who went down 1-0 at Valenciennes to Foued Kadir's second-half strike but stayed top on goal difference.
Olympique Marseille, who qualified for the Champions League last 16 earlier this week, were left in eighth place 11 points off the pace after a disappointing goalless draw at home to improving Girondins Bordeaux.
Fifth-placed Stade Rennes were also held in a 1-1 draw at home to Stade Brest while sixth-placed Toulouse beat visitors Evian Thonon Gaillard 2-1 with a last-minute goal by Umut Bulut.
France striker Gameiro, who had not scored in Ligue 1 since October 16, fired home a fine cross shot after dribbling past Sochaux keeper Teddy Richert in the 20th minute.
Despite a few pieces of individual skill from Nene and Javier Pastore, PSG looked weary after the break and coach Antoine Kombouare decided to try to hang on to their lead.
With 10 minutes left he replaced Pastore and attacking midfielder Jeremy Menez with defenders Sylvain Armand and Siaka Tiene as PSG kept their first clean sheet in six league games.
"We played well in the first half but could not keep it up after the break," PSG defender Mamadou Sakho told French TV channel Foot Plus. "But we won, so we're satisfied."
In Valenciennes, Montpellier were a pale shadow of the side that had scored seven goals in their last two games and Ligue 1 top scorer Olivier Giroud barely created a chance.
Valenciennes dominated and were rewarded a minute after the break when Geoffrey Jourdren parried David Ducourtioux's fierce shot into the path of Foued Kadir who poked the ball home.
"We failed to play our usual football," Giroud, who scored one goal and set up three more last weekend in an impressive 4-0 hammering of Lorient, told Foot Plus.
"They [Valenciennes] played it like a cup game while we were not as sharp as usual. It's a setback. Maybe, when you see you can't win a game you should just try not to lose it."