Former Continent's Best Player of the Year the Napoli star helped Nigeria establish a 3-0 lead, before they were compelled to defend resolutely for a hard-fought victory.
Nigeria weathered a dramatic comeback attempt from their opponents to progress to the last 16 of the Afcon tournament taking place in Morocco.
Jose Peseiro's side appeared to be in complete control in their pool encounter in Fes, enjoying a three-goal cushion with just 17 minutes left courtesy of strikes from their attacking trio.
However, a Tunisian defender reduced the deficit with a close-range finish from a Manchester United midfielder free-kick, igniting hopes of a turnaround.
The tension intensified when the North Africans were awarded a late penalty after a VAR check identified a handball by the Nigerian defender. The left-back converted in the dying stages to create a nail-biting conclusion.
The Carthage Eagles were inches away from a last-gasp equalizer in stoppage time, with their skipper heading a chance just past the post before a substitute guided a half-volley past the upright.
This result ensures that Nigeria, winners of the competition on three previous occasions, advance to six group points and are guaranteed top spot in their pool with a match still to be contested.
In the next round, they will meet a third-placed team from either the other preliminary groups.
In the other match, the 2004 champions stay on three points, with Uganda and Tanzania tied on a single point each after playing out a 1-1 stalemate earlier on Saturday.
The final pool matches will see Nigeria remain in the city to take on the Cranes on the next matchday, while Tunisia return to the capital to confront Tanzania.
Ali Abdi drilled home from 12 yards to give Tunisia a glimmer of hope of earning a point.
The Super Eagles, runners-up in the previous tournament, become the second team after the Pharaohs to reach the knockout stage, but coach Eric Chelle and supporters will undoubtedly be feeling relieved.
What seemed set to be a comfortable final quarter morphed into a tense affair.
Victor Osimhen had a goal disallowed for an infringement before breaking the deadlock on the stroke of half-time, expertly guiding a header into the far post from an Ademola Lookman delivery.
The lead was extended soon in the second period when Wilfred Ndidi rose highest to thump in a header from a set-piece corner.
Osimhen then turned provider his teammate for the seemingly decisive goal, only for the defender to steer a header past the Nigerian shot-stopper to begin the comeback.
The pivotal moment came when a looping cross struck the arm of the full-back, with referee Boubou Traore pointing to the spot 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 remains in their own hands; a draw against Tanzania will be sufficient to secure progression, and their coach will be keen to prevent a recurrence of the past group-stage exit that resulted in his departure.
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