The win ends Senegal's five-game winning streak in the tournament.
Nigeria sharpshooter Chamberlain Oguchi made 8 of his 13 three-pointers to lead all scorers with 28 points, while Gorgui Dieng, who played the entire 45 minutes despite being in foul trouble spearheaded Senegal's charge with 20 points and a game-high 16 rebounds.
Nigeria saw a nine-point second quarter evaporate as Ibrahima Thomas hit a three-pointer in the dying seconds of the period to give the Senegalese a 37-35 half-time lead.
Nigeria entered the final minute of regulation leading 76-73 but Dieng hit a three-pointer to tie the contest at 76-76 and send it to overtime.
Nigeria's team rotation proved crucial as their bench came up with a pivotal 21-point contribution.
With the result Nigeria, reach the AfroBasket final for the first time since 2003 and took a step closer to potentially securing claiming the sole qualifying berth for the 2016 Rio Olympics that goes to the continental champions. Teams that finish second, third and fourth will secure places in next year's FIBA Olympic Qualifying Tournaments (OQTS).
Turning Point: Oguchi hit a three-pointer with 1:07 left in overtime to give Nigeria a 82-76 that swung the game Nigeria's way for good.
Stats Don't Lie: Oguchi's three-pointers did a lot of damage to Senegal who were looking to reach the Final of the tournament for the first time since 1997, when they last won the continental title.
Game Hero: Nigeria's Olaseni Lawal stepped on floor to do whatever was needed to spark his country. By the end of the first quarter, he led his teams with 11 points.
The Bottom Line: It was a balanced contest with Nigeria capitalising on Oguchi three-point accuracy, while Senegal struggled at both ends of the floor.