Goals from Seko Fofana in four minutes of play and Jean-Philippe Krasso’s 58th-minute strike handed Ivory Coast a perfect start to Group A.
The result means that Ivory Coast sit top of Group A with three points and with two-goal advantage.
Fofana won the Man of The Match for his brilliant and commanding display on the night.
The host nation eased to the win with Fofana opening the scoring with a neat finish in just four minutes of play before Krass extended the lead for the host 13 minutes into the second half.
The Elephants, looking for their third continental triumph after wins in 1992 and 2015, had to begin their bid for glory without first-choice striker Sebastien Haller because of injury.
But midfielder Fofana broke the deadlock early on after being fed by Franck Kessie, skipping past a couple of defenders and sending his powerful right-footed strike inside the right-hand upright.
Mama Balde spurned Guinea-Bissau’s best chance in the first half, scuffing his effort when played into the box, and only a smart save by Djoco kept the score at 1-0 after the impressive Fofana latched on to a cut-back from the right.
Krasso doubled the lead after showing great skill to juggle the ball and then swivelling and hooking in a left-footed shot from eight yards out in the 58th minute.
Substitute Franculino fired straight at Ivorian keeper Yahia Fofana in the final 20 minutes but the Djurtus, who have qualified for a fourth consecutive Afcon, could not score and are still awaiting their first win at the finals.
Group A continues on Sunday with Nigeria and Equatorial Guinea facing off, before the Super Eagles meet Ivory Coast on Thursday in arguably the most-anticipated game of the group stage.