Les Elephants exited at the group stage two years ago having failed to win a match as defending champion, but they collected three points at the first attempt this time in Cairo.
Lille star Nicolas Pepe hit the bar with a first-half free-kick and Ivory Coast had to stay patient, finally getting their goal midway through the second period from Kodjia.
The goal clinched an ultimately deserved victory for Ibrahima Kamara's men, which plays Morocco next as South Africa faces Namibia.
South Africa had the first chance of note just before the half-hour mark as Thulani Hlatshwayo headed just wide of the top-left corner, but Ivory Coast built momentum heading into half-time.
Pepe saw a superb 20-yard free-kick crash away off the crossbar, before Ronwen Williams superbly saved from Kodjia at close range as the striker bore down on goal.
But Kodjia capitalised on his second big opportunity after 64 minutes, with the Aston Villa striker left completely unmarked to control and send a scruffy finish under Williams, Max Gradel with the assist.
Ivory Coast brought Wilfried Zaha off the bench in a bid to extend their lead but instead had to see out a nervy finish, although only Williams' stunning diving stop denied Pepe from making it two with another fizzing free-kick.