Captain Troost-Ekong, of Greek club PAOK, converted from the spot 10 minutes into the second half at the Ebimpe Olympic Stadium in Abidjan, after a foul on Victor Osimhen was picked up following a VAR check.
The Super Eagles then held on in front of a frenzied crowd to claim their first win in Group A after beginning their AFCON bid with a 1-1 draw against Equatorial Guinea.
Those sides are locked on four points at the top of the section, with Ivory Coast behind them on three points and Guinea-Bissau already eliminated after losing both games so far.
The fact that the four best third-placed sides in the six groups will all advance to the last 16 leaves margin for error, but Ivory Coast must now beat Equatorial Guinea in their last match on Monday to guarantee progress.
Meanwhile Nigeria must simply avoid defeat against Guinea-Bissau -– beaten 4-2 by Equatorial Guinea earlier – to ensure a top-two finish.
The match was watched by 49,517 fans, a far higher crowd than that for the hosts’ opening game, when the number of empty seats at the 60,000-capacity venue was a source of controversy.