The 20-year-old was handed his eighth appearance in the competition this season by manager Mehdi Bayat.
The Zebras started the game on the back foot after Nigeria’s Imoh Ezekiel opened the scoring for Yves Vanderhaeghe’s men in the sixth minute.
Three minutes before the interval, Osimhen turned the game around for his side by igniting the comeback with his strike in the 42nd minute.
The on-loan Wolfsburg attacker completed his brace in the 56th minute after he was set up by Gabriele Angella.
Osimhen has now scored 19 goals across all competitions this season. He was later replaced by Mali's Adama Niane with five minutes left to play.
Sporting Charleroi are set to play Antwerp in the final of the Europa League playoffs on Sunday with the aim of grabbing the final qualification ticket for the European tournament.
Nigeria are in Group B along with Burundi, Guinea and Madagascar.