Former African Footballer of the Year the Napoli star helped his team build a 3-0 advantage, but the Super Eagles were compelled to defend resolutely for a hard-fought win.
The three-time champions survived a stunning comeback attempt from Tunisia to advance to the knockout stage of the 2025 Africa Cup of Nations being held in Morocco.
Jose Peseiro's side appeared to be in complete control in their Group C clash in the Moroccan city, enjoying a 3-0 cushion with just 17 minutes remaining courtesy of strikes from their attacking trio.
Yet, Montassar Talbi reduced the deficit with a powerful header from a Manchester United midfielder free-kick, sparking hopes of a turnaround.
The drama escalated when Tunisia were awarded a late penalty after a video assistant referee review spotted a handball by Bright Osayi-Samuel. The left-back calmly slotted home in the dying stages to create a nail-biting finale.
The Carthage Eagles were inches away from a last-gasp leveler in stoppage time, with captain Ferjani Sassi directing a opportunity just past the post before a substitute sent a bobbling volley past the upright.
The victory means that Nigeria, winners of the tournament on 3 past instances, move to six group points and are guaranteed top spot in their pool with a match still to play.
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, the 2004 champions remain on three points, with Uganda and Tanzania tied on one point after registering a 1-1 draw in the day's other fixture.
The concluding pool matches will see the group leaders remain in Fes to take on the Cranes on Tuesday, while the Eagles of Carthage travel back to Rabat to face Tanzania.
Ali Abdi drilled home from 12 yards to give Tunisia a glimmer of hope of earning a point.
Nigeria, runners-up in the 2023 tournament, become the next team after the Pharaohs to reach the knockout stage, but their manager and fans will certainly be feeling relieved.
What seemed set to be a comfortable last period transformed into a tense conclusion.
The prolific striker had a goal disallowed for offside before breaking the deadlock on the stroke of half-time, expertly guiding a glancing effort into the far post from an Atalanta winger cross.
The lead was extended early in the second half when the Leicester City midfielder climbed above everyone to power home a header from a Lookman corner.
Osimhen then turned provider his teammate for the seemingly decisive goal, before Montassar Talbi to steer a header past the Nigerian shot-stopper to begin the comeback.
The key incident arrived when a looping cross hit the arm of Bright Osayi-Samuel, with referee Boubou Traore awarding a penalty after reviewing the pitchside screen.
Despite the defender's confident conversion, the 2004 champions in the end fell short of pulling off a remarkable recovery.
Tunisia's destiny is still in their control; a draw against Tanzania will be enough to see them through, and manager Sami Trabelsi will be keen to prevent a repeat of the past early elimination that resulted in his departure.
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