Moses Simon was the Nigerian scorer in a 1-0 victory in Bissau, converting a 30th-minute penalty after Fali Cande fouled Bright Osayi-Samuel.
Simon fired the spot-kick into the right corner of the net as goalkeeper Jonas Mendes dived in the opposite direction.
Desperate for revenge after a solitary-goal loss to much lower-ranked Guinea-Bissau in Abuja last Friday, Nigeria looked likely winners for most of the top-of-the-table Group A clash.
Prolific Napoli scorer Victor Osimhen turned smartly in the penalty area as the hour mark approached only to see his low shot rebound off the far post.
Portuguese coach Jose Peseiro made five changes after the Abuja debacle with Nice forward Terem Moffi among those promoted.
But the scorer of 15 Ligue 1 goals this season did not impress and was replaced midway through the second half.
Victory returned Nigeria to first place with nine points after four rounds, followed by Guinea-Bissau (seven), Sierra Leone (five) and Sao Tome e Principe (one).
For the second time in five days, Algeria made hard work of defeating Niger, with a sixth-minute Baghdad Bounedjah goal producing a 1-0 win near Tunis.
The match-winner was set up by Manchester City winger Riyad Mahrez, whose late goal delivered a 2-1 win in Algiers last week.
Coach Djamel Belmadi retained only Mahrez, AC Milan midfielder Ismael Bennacer and Nantes forward Andy Delort for the rematch.
Algeria have 12 points in Group F and are assured of a top-two finish and qualification for the finals next January and February.
Precious Ghana point
The Desert Foxes are the third qualifiers for the 24-nation tournament after shock 2022 World Cup semi-finalists Morocco and the Ivory Coast, who are guaranteed a place as hosts.
Tanzania have four points, Niger two and Uganda one in the three-way race for the other ticket to Abidjan from the section.
Ghana earned a precious Group E point by forcing a 1-1 draw with Angola in Luanda, where a Lucas Joao goal off a penalty soon after half-time was cancelled by Osman Bukari.
Serbia-based Bukari made an instant impact as a substitute, with his 72nd-minute equaliser arriving less than 60 seconds after coming on.
The Central African Republic, one of 10 countries never to qualify for the Cup of Nations, climbed above Angola to second after a 2-0 win over Madagascar in Douala.
Louis Mafouta scored twice against the Indian Ocean side last week, and repeated the feat as the Wild Beasts completed a double.
Four-time African champions Ghana have eight points, Central African Republic seven, Angola five and Madagascar one with the final two rounds scheduled for June and September.
South Sudan, another nation seeking a first appearance at the African football showpiece, suffered a Group G setback after conceding a late goal to lose 1-0 against Congo Brazzaville.
It was the third defeat in four matches for the Bright Stars and relegated them to last place, six points behind pacesetters Mali and three below second-placed Congo.
Guinea top Group D thanks to a 3-2 victory over Ethiopia in Rabat with Liverpool midfielder Naby Keita scoring the winners’ first goal after only four minutes.