Sangante emphatically turned a Moses Simon cross into his own net in the 36th minute, after feeling compelled to intervene with Victor Osimhen lurking behind him.
The result means the Super Eagles qualify in second place in Group A with seven points, behind Equatorial Guinea whose 4-0 destruction of hosts Ivory Coast leaves them with a far better goal difference.
Nigeria, who drew 1-1 with Equatorial Guinea in their opening game, have since been efficient if not spectacular, defeating the Ivorians 1-0 with a William Troost-Ekong penalty before this result.
Jose Peseiro's team will now stay in Abidjan for a last-16 tie on Saturday at the Felix Houphouet Boigny Stadium against the runners-up in Group C, which will be Senegal, Guinea or Cameroon.
Nigeria's domination had been sterile before the goal came, but they should have added to their lead after the break.
African player of the year Osimhen and substitute Zaidu Sanusi both had goals disallowed for offside in the second half, while Calvin Bassey had a penalty appeal turned down and Ola Aina blasted a good chance over.
Franculino Dju had a goal ruled out at the other end for Guinea-Bissau, who were already eliminated before this game and finish with three defeats.
Shock winners away to Nigeria in qualifying last March, they have still never won a game in 12 attempts across four appearances at the Cup of Nations itself.
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