Stand-in captain Joseph Yobo put the Super Eagles ahead in the eighth minute of extra time, opening the way for teammates Yakubu Aiyegbeni and Ahmed Garba to score in quick succession and complete the tally for the hosts, all within five minutes.
Nigeria, which dispatched arch-rival Ghana in the tournament opener on Friday, dominated play right from kickoff. But the African champions proved indomitable all through regulation time as they warded off all attempts by the Eagles to score.
The pressure eventually got to the visitors, who had two players sent off for rough play, a development which weakened the team during the extra time and made it an easy prey for the Eagles.
Both teams had to endure treacherous playing conditions, caused by a continuous downpour that soaked the patchy turf of the National Stadium venue.
It was sweet revenge for the Super Eagles, who were devoured by the Indomitable Lions in the final of the 2000 African Nations Cup at the same venue.
Nigeria got the LG tournament winner's prize of $50,000 while Cameroon received $30,000.
Ghana, which was awarded third place after the classification tie with defending champion Iran failed to hold, went home with $20,000.
Nigeria's Yakubu Aiyegbeni, who scored three goals in the tournament, was voted the Most Valuable Player while Cameroon's Eric Kwekeu was named best goalkeeper.
The tournament is named after its official sponsor, L-G Electronics, which was also one of the official sponsors of the recent Cricket World Cup in South Africa.
The Super Eagles will next host the Flames of Malawi on Saturday in Abuja in a 2004 African Nations Cup qualifier. The Super Eagles lead their qualifying group with four points from two matches, and are the favourites to advance to the finals in Tunisia.