Angola went into the game looking to win a 12th African title, but some poor shooting boosted Nigeria's confidence as they led by as many as 19 points.
The win also saw Nigeria qualify for the 2016 Rio de Janeiro Olympics.
Paced by Chamberlain Oguchi and Olaseni Lawal, Will Voigt's team closed their campaign with a 6-1 mark, while the Angolans return home with a 5-2 record.
Oguchi hit a trifecta of three-pointers on his way to a game-high 19 points.
Despite a modest shooting night, Carlos Morais led the Angolans with 15 points, Yanick Moreira added 13 and Braulio Morais, who fouled out, contributed a dozen off the bench.
The Angolans jumped to an early 7-1 lead in the opening seven minutes of the game, but the Nigerians' team rotation made the difference as they turned the score around in the second quarter.
Angola's 12 personal fouls in the second quarter allowed Nigeria to go to the free-throw line 16 times, dealing a big blow to the 2013 champions.
Lawal proved too much for the Angolans as he dominated the painted area with 12 points and 5 offensive rebounds.
Usually, a poor free-throw shooter, he made all six of his attempts from the foul line.
Although Angola cut the deficit to just seven in the third quarter, Nigeria regrouped in time to stay comfortably ahead for the remainder of the contest.
Turning Point: Oguchi hit a three-pointer that gave Nigeria a 23-19 lead with 3:28 minutes in the second quarter, and the Nigerians went on close the half leading 37-24.
Stats Don't Lie: Nigeria capitalised from their athleticism to out-rebound Angola 60-37. The former champions paid the price for making only 8 of their 16 free-throws.
Game Hero: Lawal ruled the painted area, and the Angolans were never able to stop him.
The Bottom Line: Ever since Nigeria took the lead in the second quarter, Angola were never the same, showing inexplicable distress. Angola’s poor ball movement was also costly as came up with only seven assists.