How Super Eagles humble the Falcons
Samuel Chukwueze struck in the third minute in Garoua and Taiwo Awoniyi doubled the lead by scoring his first Nigeria goal on the stroke of half-time.
Moses Simon added a third right at the start of the second half, with Walieldin Khidir converting a consolation spot-kick for Sudan.
Nigeria top the section with six points ahead of their final group game against Guinea-Bissau on Wednesday. Sudan have one point and must beat record seven-time champions Egypt to potentially advance.
Former Super Eagles star Augustine Eguavoen, in temporary charge after last month's sacking of German coach Gernot Rohr, stuck with the same line-up that defeated Egypt 1-0 in their opening game.
Nigeria took control with barely two minutes gone when Nantes winger Simon controlled a long throw into the box by Ola Aina, teeing up Chukwueze to steer past Sudan goalkeeper Ali Abu Eshrein.
William Troost-Ekong, the Nigeria captain, saw his volley kept out superbly from a free-kick, and Sudan rode their luck again moments later when Joe Aribo hit the post and Simon poked the rebound against a defender sat on the line.
Nigeria grabbed a second goal in slightly fortunate circumstances as Troost-Ekong headed Kelechi Iheanacho's cross against a defender, the ball ricocheting off the head of Awoniyi and squirming in under the keeper.
Simon all but secured the victory 34 seconds after half-time when he combined with Awoniyi before tapping home after bursting into the area.
Sudan cut the deficit 20 minutes from time when they were awarded a penalty following a VAR review as Aina was punished for a foul on Mustafa Mohammed, with Khidir tucking away from the spot.The Super Eagles will take on Guinea-Bissau in their last group game on the 19th of January.