Gameiro netted from Jeremy Menez's pass to move PSG on 58 points from 27 games, one ahead of Montpellier who beat Caen 3-0 at home later on Sunday.
PSG midfielder Sissoko was shown a straight red card for a challenge on Eric Bautheac four minutes before half-time.
PSG brushed off their numerical disadvantage and went ahead four minutes after the restart in a move started and finished by defender Siaka Tiene who converted a Guillaume Hoarau cross.
Dijon equalised on 76 minutes when Steven Paulle headed in a Gael Kakuta cross before Gameiro had the last word for PSG.
"It was a tough match. After Sissoko's red card, it was tough. The team was strong mentally," coach Carlo Ancelotti said.
Second-half goals from Karim Ait-Fana, Souleymane Camara and Ligue 1 top-scorer Olivier Giroud eased Montpellier to victory over strugglers Caen with only a fine performance from goalkeeper Alexis Thebaut preventing a heavier defeat.
Thebaut made a series of superb saves and Montpellier struck the woodwork three times Ait-Fana finally broke through on 51 minutes.
Camara stole the ball from defender Aurelien Montaroup to double the lead in the 83rd minute and Giroud added a third from the penalty spot, his 17th goal of the campaign.
Montpellier's victory took them a step closer to automatic Champions League qualification after third-placed Lille lost at Olympique Lyon 2-1 on Saturday. Lille now trail Montpellier by 10 points.
Stade Rennes moved up to fifth place despite being held to a 1-1 draw at home by relegation-threatened Auxerre.
The hosts needed a 66th-minute goal from Yacine Brahimi to earn a point after Dennis Oliech's early goal for Auxerre.
