The 2018 World Cup hosts who are preparing for the Confederations Cup in June were overpowered and outplayed by the 2015 African champions.
The Elephants won their first game since their humiliating attempt to defend their Afcon title in Gabon last January saw them exit without a win in the group stage.
Under caretaker handler Ibrahim Kamara, Cote d’Ivoire held their own in chilly conditions to notch their first win since the misadventure of Gabon.
Aston Villa striker Kodjia scored first on the half hour mark before Zaha added the second on 70 minutes.
Russia had no answer for the Ivoirians with Sylvain Gbohouo standing between Alexander Bukharov’s attacking runs and goal.
Russia are struggling to put together a winning side under coach Stanislav Cherchesov ahead of June’s Confederations Cup kick off.
The Bears have lost recent friendly matches to Costa Rica and Qatar. They defeated Ghana 1-0 in September as well as Romania in November.
Russia are ranked 60th in the world and were racked by the fan rampage that took place during the 2016 European Championships in France.
They will face Belgium in another friendly next Tuesday in Sochi, the site of the 2014 Winter Olympic Games.
Cote d’Ivoire will take on Senegal in Paris on Monday in an international friendly.