The victory sees the Elephants’ lead the pack with three points after Gabon and Morocco settled for a barren draw in group’s other fixture earlier in Franceville.
The new generation Elephants squad gave their fans a reason to believe in their abilities to deliver, with a performance that takes them to the summit of the standings after the First Day of matches.
The visitors stunned the home crowd with the first goal on 18 minutes courtesy Yatabare, who got the better of Eric Bailly before sliding past onrushing Sylvain Gbohouo.
The Elephants responded in style eight minutes later when a Franck Kessie pass found Kodjia, who controlled nicely before firing past Mali goalkeeper Oumar Sissoko.
The equalizer was what the Ivorians needed as they pressed further in search of more goals. On the half-hour mark, right-back Serge Aurier during one of surges upfront laid a cross into the Malian area and Coulibaly in his bid to clear the ball safety shot into his own net.
Four minutes later, Gervinho made his experience count with a superb volley on the turn from his left that Sissoko had no answers to.
The second half was a balanced game with both teams failing to find the net amidst series of substitutions from either side.
The Ivorians next travel to Marrakech to face Morocco on Match Day Two on 12 November 2016, whilst Mali battles Gabon same day in Bamako.
Elsewhere in Ouagadougou, Burkina Faso left it late to hold visiting South Africa 1-1 in Group D. Dean Furman fired the South Africans into the lead on 80 minutes before Banou Diawara levelled in stoppage time.