The Super Eagles, playing in the tournament finale for the seventh time, took the lead through Sunday Mba in the 40th minute and held on to secure their third continental crown, and their first since 1994.
The result ended a dream run from the Berkinabe, who reached the semifinals for only the second time in their history, before edging Ghana on penalties to book their place in the gold medal match.
Mali beat Ghana 3-1 in the third-place playoff in Port Elizabeth on Saturday.
Player of the match – Mikel Obi
Highest goal scorer of the competition – Emmanuel Emenike