Ranked 15th by Fifa, the Elephants were facing a team placed 145th on the world table, but the visitors stunned many by standing up against the Ivorian challenge marshalled by Didier Drogba, Kolo Toure, Chieck Tiote and Gervinho.
Salomon Kalou put the home side in the lead nine minutes into the game after finding a breach in the Tanzanian area during a goalmouth scramble.
However, the visitors remained unperturbed and kept disorganising the Ivorians with their two-to-one attacking style, which kept the hosts’ attacking line unproductive for the rest of the first half.
Tanzania’s Ambross Aggrey Morris was shown a red card for pulling down an Ivorian striker, compounding issues for the visitors, who could not alter the scoreline in their favour until the end of the meeting.
Cote d’Ivoire will play Morocco in Marrakech on June 9 while Tanzania will host Group C’s fourth member Gambia in Dar es Salaam on June 10.