Former African Footballer of the Year the Napoli star helped Nigeria establish a 3-0 advantage, before the Super Eagles were compelled to hold on for a narrow win.
Nigeria weathered a dramatic comeback attempt from Tunisia to advance to the last 16 of the Afcon tournament taking place in Morocco.
The Super Eagles seemed to be in complete control in their Group C clash in Fes, holding a 3-0 cushion with only a quarter of an hour left courtesy of strikes from their attacking trio.
Yet, Montassar Talbi reduced the deficit with a close-range finish from a Hannibal Mejbri free-kick, sparking hopes of a recovery.
The tension escalated when Tunisia were given a spot-kick after a video assistant referee check identified a handball by Bright Osayi-Samuel. Ali Abdi calmly slotted home in the 87th minute to set up a nail-biting finale.
The Carthage Eagles came agonizingly close from a stunning equalizer in added time, with captain Ferjani Sassi heading a opportunity narrowly wide before Ismael Gharbi sent a half-volley past the upright.
This result ensures that the Super Eagles, champions of the competition on three past instances, advance to six group points and are guaranteed top spot in Group C with a match still to play.
For the round of 16, they will meet a third-placed side from either Group A, B or F.
Meanwhile, the 2004 champions remain on three points, with the East African teams tied on a single point each after playing out a 1-1 draw in the day's other fixture.
The final group matches will see the group leaders remain in the city to play Uganda on the next matchday, while the Eagles of Carthage return to Rabat to face the Taifa Stars.
The Tunisian defender drilled home from the penalty spot to offer his team a glimmer of hope of earning a point.
The Super Eagles, runners-up in the 2023 edition, become the next nation after Egypt to reach the next phase, but their manager and supporters will certainly be breathing a sigh of relief.
What looked like set to be a comfortable final quarter transformed into a nerve-wracking affair.
The prolific striker had a goal disallowed for an infringement before breaking the deadlock on the stroke of the interval, expertly guiding a glancing effort into the bottom corner from an Ademola Lookman cross.
The lead was doubled soon in the second period when the Leicester City midfielder climbed above everyone to thump in a powerful nod from a set-piece kick.
Osimhen then set up his teammate for the seemingly decisive goal, only for Montassar Talbi to direct a header past the Nigerian shot-stopper to begin the comeback.
The key incident arrived when a high ball struck the forearm of Bright Osayi-Samuel, with the official awarding a penalty after consulting the VAR monitor.
Despite the defender's confident conversion, Tunisia in the end came up just short of completing a stirring recovery.
Tunisia's destiny is still in their own hands; a draw against Tanzania will be enough to secure progression, and manager Sami Trabelsi will be eager to prevent a repeat of the past early elimination that resulted in his previous resignation.
Elara Vance is a tech journalist with over a decade of experience covering AI, cybersecurity, and emerging technologies across Europe.