The Auriverdes took the lead five minutes into the second half when captain Fabio chipped a superb shot into the net with only goalkeeper to beat.
Nigeria fought back with Osanga King's equaliser in the 63rd minute before Chrisantus Macauley made it 2-1 for the Golden Eaglets with only five minutes remaining. Their joy was shortlived, however, as Atila Araujo levelled matters once again in the 88th minute.
The Brazilians soaked up the pressure in extra time and kept their nerve to win 4-3 on penalties.
Captain Fabio was arguably the most valuable player of the tournament. The attack-minded left-back stole the show from playmaker Lulinha, as he showed remarkable talent on the ball and a range of accurate passes. He also scored the opening goal in Brazil's first game against the hosts and added another in the final.
Brazil's newly appointed coach, Luiz Antonio Nizzo was satisfied with winning his first tournament in charge of the team. "We've managed to get past strong opponents from all over the world," he said. "Nigeria were physically stronger than ourselves but if we can concentrate on our game and take advantage of our skills like we did today, we will be able to beat anyone in August."
For their part, Nigeria reached the final in style, winning three games in a row against New Zealand (2-1), USA (2-1), and Japan (5-0) to eventually become the tournament's highest scorers with 11 goals.
The Golden Eaglets arrived in Korea without inspirational playmaker Ibrahim Rabiu. But captain Ademola Rafeal made up for his absence in midfield, while King and Macauley combined effectively up front.
Japan had been off to a flying start to this tournament, with two straight wins over USA (1-0) and New Zealand (3-0). However, after a shock defeat by Nigeria (0-5) in their last group game, they had to prepare for the third place play-off against their arch-rivals.
"We were under pressure after the heavy defeat," admitted coach Hiroshi Jofuku, whose team defeated Korea Republic last year in the AFC U-16 Championship on the way to winning the Asian title. "We knew our opponents so well we could press them from midfield. But there's still room for improvement before the finals."
"We gained confidence from the games with Brazil and Ghana," said Korea Republic coach Park Kyung-Hoon. "We've found our strengths as well as weaknesses. Our priority is to organise the team perfectly as a unit, because we don't have one outstanding player in the squad. We also need more strength, both physically and mentally."