Goals from Franculino Dju, Mama Balde and Alvaro Djalo handed the Djurtus their biggest victory over the Super Eagles and strengthened their position at the top of Group L.
Coach Eric Chelle made three changes to his starting line-up, introducing Bright Osayi-Samuel, Frank Onyeka and Taiwo Awoniyi.
The three-time African champions nearly made the perfect start when Ademola Lookman connected with Alex Iwobi's pass in the 14th minute, but his left-footed effort was saved.
However, the hosts struck just a minute later after Franculino collected possession on the left, cut inside and curled a fine effort beyond Stanley Nwabali.
Onyeka subsequently hit the side netting as Nigeria searched for an equaliser, while Nwabali denied Beto shortly before half-time.
Chelle introduced Moses Usor and Moses Simon at the interval, replacing Onyeka and Awoniyi to revive Super Eagles’ attack.
Both substitutes had opportunities to restore parity, but their efforts were comfortably saved.
Guinea-Bissau punished the visitors’ wastefulness in the 66th minute when Balde beat Osayi-Samuel to double the hosts' advantage.
Tolu Arokodare and George Ilenikhena subsequently squandered opportunities to reduce the deficit before Djalo completed the rout in the fifth minute of stoppage time.
The defeat was Nigeria's first against African opposition by a three-goal margin since their 5-1 loss to Algeria at the 1990 AFCON.
It also revived memories of September 2014, when Congo stunned the Super Eagles 3-2 at home in an AFCON qualifier. Nigeria subsequently failed to qualify for the 2015 tournament.
Guinea-Bissau now lead Group L with six points and a goal difference of +5, while Nigeria remain second with three points and a -2 goal difference.
With Tanzania already guaranteed a place at the tournament as co-hosts, the Super Eagles face a difficult battle with the Djurtus and the Barea for the group's remaining qualification spot.