Seko Fofana gave the Elephants the perfect start in the Group A clash in Abidjan when he blasted home from just inside the area in the fourth minute.
He almost doubled the lead before half-time but another powerful effort was tipped on to the bar by Ouparine Djoco.
Jean-Philippe Krasso hooked in the second after the break after some smart control under pressure in the box.
The 2023 Afcon finals have been pushed back by six months - into early 2024 - to avoid the rainy season in West Africa, but the delay helped Ivory Coast finalise their preparations, with the total cost of hosting more than $1bn.
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.
Nigeria face Equatorial Guinea at 14:00 GMT on Sunday in the second Group A match, while 2021 runners-up Egypt and four-time champions Ghana will also be in action later in the day as Group B commences.