Kadir, signed on loan from Marseille last month, marked his home debut with two well-taken goals, the first coming after 13 minutes as he cut inside onto his right foot before curling an effort beyond the reach of Ajaccio goalkeeper Guillermo Ochoa.
The Algeria international winger then virtually sealed the win for the Brittany club three minutes later, slotting past Ochoa again after collecting a long free-kick from Jean II Makoun and shrugging off the attentions of full-back Benjamin Andre.
The result leaves Fabrizio Ravanelli's Ajaccio winless after their first six games, while Rennes are now level on points with fourth-placed Marseille, who could only manage a 0-0 draw with Bastia.
Elie Baup's team travelled to Corsica without a win in their last three competitive matches, and were hoping to bounce back from a 2-1 UEFA Champions League defeat to Arsenal on Wednesday.
Rene Girard's side took the lead 11 minutes before the break, despite early pressure from Sochaux, as striker Nolan Roux found the bottom corner after being played in by Salomon Kalou.
By contrast, Girard's former club Montpellier have only one win to their name this term after they threw away a two-goal lead at Evian, who fought back to earn a 2-2 draw at the Parc des Sports in Annecy.
Meanwhile, at Stade Auguste-Delaune II, Reims and Guingamp played out a 1-1 draw as Nicolas de Preville's spectacular bicycle-kick secured a point for the hosts after an Anthony Weber own-goal had put the visitors in front.
