Samuel Chukwueze set the ball rolling for the Super Eagles in the third minute from a Moses Simon pull-back.
Nigeria doubled their lead on the stroke of half-time when the ball went in off Taiwo Awoniyi and Simon rolled in a third straight after the restart.
Walieldin Khedr pulled a goal back for Sudan from the penalty spot after Ola Aina was penalised for a challenge.
The Nigeria right-back was adjudged to have fouled Secretary Birds defender Mustafa Karshoum, pulling his shirt as a corner was swung in, following a video assistant referee review.Nigeria had won their Group D opener against Egypt 1-0, and the result against a side ranked 125th in the world was never in doubt after Villarreal forward Chukwueze slotted into the bottom left-hand corner from the centre of the box.
The Nigeria Football Federation’s decision to replace long-serving coach Gernot Rohr just four weeks before the tournament looks to have paid off, as interim boss Augustine Eguavoen once again saw his side put in a largely dominant performance in Garoua.
The second was a somewhat freak goal, as a clearing header from Salaheldin Nemer cannoned in off Awoniyi, but the West Africans could have had further first-half goals as William Troost-Ekong had an effort blocked and Joe Aribo hit the post.
The Super Eagles, who are chasing a fourth Nations Cup triumph, know they will face a third-placed side in the last 16 if they can top Group D, and they round off their group campaign against Guinea-Bissau on Wednesday (19:00 GMT).
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