Former Continent's Best Player of the Year the Napoli star was instrumental in Nigeria establish a 3-0 lead, but the Super Eagles were forced to hold on for a hard-fought win.
The three-time champions weathered a stunning late rally from Tunisia to progress to the knockout stage of the Afcon tournament being held in the host nation.
Jose Peseiro's side appeared to be cruising in their Group C encounter in Fes, holding a 3-0 cushion with only a quarter of an hour remaining thanks to strikes from their attacking trio.
However, a Tunisian defender pulled one back with a powerful header from a Manchester United midfielder set-piece, igniting hopes of a recovery.
The drama intensified when the North Africans were awarded a spot-kick after a video assistant referee check identified a handball by the Nigerian defender. The left-back converted in the dying stages to create a frantic finale.
Tunisia were inches away from a last-gasp equalizer in stoppage time, with their skipper heading a chance narrowly wide before a substitute sent a half-volley past the goal frame.
The victory means that Nigeria, winners of the tournament on three past instances, move to 6 points and are guaranteed first place in Group C with one game still to be contested.
For the round of 16, they will face a third-placed side from either the other preliminary groups.
Meanwhile, Tunisia stay on 3 points, with Uganda and Tanzania tied on one point each after registering a 1-1 draw earlier on Saturday.
The concluding pool fixtures will see the group leaders stay in the city to take on the Cranes on the next matchday, 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 draw.
Nigeria, finalists in the previous edition, become the next team after the Pharaohs to qualify for the next phase, but coach Eric Chelle and fans will undoubtedly be breathing a sigh of relief.
What looked like set to be a straightforward final quarter morphed into a tense conclusion.
The prolific striker had a goal disallowed for an infringement before breaking the deadlock right before the interval, expertly guiding a header into the far post from an Ademola Lookman delivery.
The advantage was doubled early in the second period when Wilfred Ndidi climbed above everyone to power home a powerful nod from a set-piece corner.
Osimhen then set up his teammate for the third goal, before the defender to direct a powerful header past the Nigerian shot-stopper to initiate the comeback.
The key incident came when a high ball struck the forearm of the full-back, with referee Boubou Traore awarding a penalty after reviewing the VAR monitor.
Although Ali Abdi's confident conversion, Tunisia in the end fell short of completing a remarkable recovery.
Tunisia's destiny is still in their control; a point against Tunisia will be enough to see them through, and manager Sami Trabelsi will be eager to prevent a repeat of the past group-stage exit that led to his departure.
A seasoned casino analyst with over a decade of experience in gaming strategies and industry trends.
