Yaya Banana opened the scoring for the Indomitable Lions, heading low into the net from Karl Toko Ekambi’s cross.
Stephane Bahoken capitalised on a defensive mix-up three minutes later to seal the points for Clarence Seedorf’s side.
Ghana drew 2-2 with Benin in Tuesday’s other Group F game.
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Cameroon’s tournament preparations were disrupted by a row over bonuses, with the Indomitable Lions squad staging a sit-in protest before departing for Egypt.
The five-time winners started slowly in Ismailia but grew into the game as the first half progressed, spurning several good opportunities to break the deadlock before the interval.
Christian Bassogog twice failed to hit the target from good positions, while Fulham midfielder Andre-Frank Zambo Anguissa sidefooted wide from Bassogog’s pass.
Full-back Joyskim Dawa Tchakonte and captain Eric Maxim Choupo-Moting both forced fine saves out of Guinea-Bissau goalkeeper Jonas Mendes, before quick-fire goals from Banana and Bahoken secured the win.
Piqueti went closest for Guinea-Bissau, heading against the post from Nadjack’s delivery.
Cameroon are next in action against fellow tournament favourites Ghana on Saturday (18:00 BST), while Guinea-Bissau take on Benin later that day (21:00 BST).
By BBC Sport Africa’s Piers Edwards
This was a solid start from the defending champions, who took a while to get into their stride – helped by Guinea-Bissau running out of steam a little in the second half.
That was perhaps unsurprising after Guinea-Bissau – taking on the five-time champions in only their second finals appearance – impressed when holding their own in the first half, albeit helped by some wayward finishing from the champions.
That was a theme of the game as the Indomitable Lions missed chance after chance – but two goals in three minutes changed their fortunes (the second fortuitously falling their way) – as they slowly went up the gears.
Surprise champions in 2017 after several big-name players missed the tournament, Cameroon have been bolstered by the return of Ajax’s Andre Onana and Paris St-Germain’s Eric Maxim Choupo-Moting – but opponents will have noticed some defensive lapses which Guinea-Bissau failed to exploit.