Former Continent's Best Player of the Year the Napoli star helped his team establish a 3-0 lead, before they were forced to hold on for a narrow win.
The three-time champions weathered a dramatic late rally from their opponents to advance to the last 16 of the Afcon tournament being held in the host nation.
Jose Peseiro's side appeared to be in complete control in their Group C clash in Fes, enjoying a three-goal cushion with just a quarter of an hour left thanks to goals from their attacking trio.
Yet, a Tunisian defender pulled one back with a powerful header from a Hannibal Mejbri free-kick, igniting hopes of a turnaround.
The tension escalated when the North Africans were awarded a spot-kick after a VAR check identified a handling offense by Bright Osayi-Samuel. Ali Abdi converted in the 87th minute to create a nail-biting finale.
Tunisia were inches away from a last-gasp leveler in added time, with their skipper directing a chance just past the post before a substitute guided a bobbling volley wide of the upright.
This result means that the Super Eagles, winners of the tournament on 3 previous occasions, move to 6 points and are guaranteed top spot in their pool with a match left to be contested.
For the round of 16, they will meet a best third-place team from one of Group A, B or F.
In the other match, Tunisia remain on three points, with Uganda and Tanzania tied on one point after registering a one-all stalemate earlier on Saturday.
The final group fixtures will see the group leaders stay in Fes to play Uganda on Tuesday, while the Eagles of Carthage travel back to Rabat to face Tanzania.
Ali Abdi smashed home from 12 yards to give Tunisia a glimmer of hope of earning a point.
The Super Eagles, runners-up in the previous edition, are the second team after Egypt to reach the knockout stage, but their manager and supporters will certainly be feeling relieved.
What seemed set to be a comfortable final quarter transformed into a nerve-wracking affair.
The prolific striker had a effort ruled out for an infringement before breaking the deadlock on the stroke of half-time, expertly guiding a header into the bottom corner from an Ademola Lookman delivery.
The lead was extended soon in the second period when the Leicester City midfielder rose highest to thump in a powerful nod from a Lookman kick.
Osimhen then set up Lookman for the third goal, only for the defender to direct a powerful header past the Nigerian shot-stopper to initiate the comeback.
The pivotal moment arrived when a high ball struck the forearm of Bright Osayi-Samuel, with referee Boubou Traore pointing to the spot after consulting the VAR monitor.
Although the defender's confident conversion, the 2004 champions in the end fell short of pulling off a remarkable recovery.
Their fate is still in their own hands; a draw against Tunisia will be sufficient to secure progression, and their coach will be keen to prevent a recurrence of the 2013 group-stage exit that led to his departure.
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