The winner came when Opa Sangante diverted a Moses Simon cross into his own net nine minutes before the break.
Both sides had goals ruled out in the second half for offside, while Nigeria striker Victor Osimhen also had an effort disallowed for handball.
Jose Peseiro’s side finished second in Group A behind Equatorial Guinea, who beat hosts Ivory Coast 4-0.
The Super Eagles will face the second-placed side from Group C, which will be Senegal, Guinea or Cameroon, in the last 16 on Saturday (20:00 GMT).
Meanwhile, Bouchra Karboubi became the second woman to referee an Afcon finals game, following in the footsteps of Salima Mukansanga in Cameroon two years ago, with the Moroccan also making history by heading the first all-female officiating team at the finals.
Osimhen misfires but Nigeria ease through
Guinea-Bissau had no chance of progressing to the knockout stages, but played their part in an entertaining match at Felix Houphouet-Boigny Stadium.
In some respects it was a game to forgot for African footballer of the year Osimhen, who failed to bury any of the opportunities he had to score.
However, the Napoli striker played his part in the only goal after Simon launched a darting run down the left.
The winger drilled a low ball into the path of Osimhen which Sangante had to deal with some seven yards out, but the centre-back ended up smashing the ball into his own net.
Osimhen closed the first half by missing a good chance as he headed wide after meeting a cross from the left wing, and the story of the second half was once again one of Nigeria pushing forward while Guinea-Bissau sat back and lacked spark in attack.
Minutes after Osimhen headed a cross from Ola Aina wide, Baciro Cande’s side counter-attacked and Dalcio forced Stanley Nwabali into a low save.
Osimhen thought he had finally scored to double Nigeria’s lead in the 59th minute when he turned Bright Osayi-Samuel’s cross into the net from close range, but the officials spotted he had clearly handled the ball prior to putting it into the net.
Victor Osimhen endured a frustrating time in front of goal, and failed to add to his strike against Equatorial Guinea in Nigeria’s opener
Alex Iwobi side-footed wide for the Super Eagles before Nwabali had to claw away Fali Cande’s dipping free-kick and Nito Gomes diverted wide from the resulting corner.
Guinea-Bissau forward Franculino rifled in a rising shot in the 83rd minute after a run through the middle, but that goal was ruled out for offside and a minute later Nigeria saw another effort chalked off.
Osimhen’s low shot across goal was saved by Jonas Mendes before substitute Zaidu Sanusi converted the rebound, but the flag went up for an offside earlier in the move.
Ivory Coast’s surprising collapse in the other Group A game meant a point would have been enough for Nigeria to progress, but Jose Peseiro will be aware that his side will need to be more clinical in attack if the West Africans are to go deep at the finals.
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