The Elephants top Group B with six points as they guaranteed a spot in the next round even if they lost to Mali, who lie second on four points, in the last group stage game.
Nigeria are in a critical situation, having only collected one point from possible six.
They need to beat Benin while hope that Ivory Coast maintain their 100% record at the expense of Mali to have any chance of progressing.
The first-half was a very dull affair, with both sides struggling to break through tight defenses.
Obafemi Martins' low shot after 17 minutes was easily collected by Mali keeper Mahamadou Sidibe.
Seydou Keita had a decent shot blocked by Nigeria guardian Austin Ejide two minutes after restart.
Yakubu Ayegbeni thought he had opened the scoring for Nigeria in the 79th minute when he tapped-in from close range, but his strike was ruled out for offside.
Eight minutes from time, Keita was unlucky to see his fierce drive denied by the crossbar.