Gian's winner followed an equally decisive and flamboyant finish by Julian Joachim which secured England third place with a 2-1 win over the hosts, Australia.
The goal by Gian was a fitting finale to a game of high quality in which Brazil, the cup favourites, came back from a half-time deficit to win a record third victory in the under-20 tournament.
The final was in contrast - Joachim's goal apart - to the error- strewn performances from two exhausted sides in the curtain-raiser at the Sydney Football Stadium, which brought into question the wisdom of forcing young players to play a meaningless match at the end of a hard competition.
Ghana, appearing in the 16-nation cup for the first time, took the lead in the 12th minute through a spectacular header from their youngest player, Emmanual Duah. The goal by the 16-year-old Duah, who is on Torino's books, was only the sixth conceded by the Brazilians in 23 internationals.
The Ghanaians, playing with six members of the side who won the under-17 cup two years ago and with the Anderlecht midfielder Nii Lamptey dominating, deserved to be ahead at the break.
They faced a different Brazil after the interval and the South Americans got the goal they needed within four minutes. The gifted midfielder Adriano, strangely subdued in the first half, threaded a ball through the Ghanaian defence for Yan to push past the goalkeeper Ben Owu.
The equaliser clearly unsettled Ghana who had two players booked when Brazil were awarded a free-kick just outside the area. In all, three Ghanaians and two Brazilians were booked.
Brazil asserted their superiority and blunted Lamptey's skills with some tight marking, but the match seemed destined to go into sudden-death extra time when Gian struck. He latched on to a pass from his captain, Marcelinho, and hit a fierce drive past Owu which had the 40,000-crowd on its feet.
Sao Paulo's Adriano, 17, who was joint top-scorer in the tournament with three goals, was later named the championship's best player. He moves to the Swiss side Neuchatel Xamax next week.
Julio Leal, Brazil's coach, described the victory as a return to his country's best brand of football which augured well for the senior side. 'In my team there could possibly be three players in the 1994 World Cup,' Leal said.
Leal's boys of '94 could well be joined in America by Joachim. His virtuoso effort for England was on a par with his goal for Leicester against Barnsley in the FA Cup. This time he beat three defenders and then finished well after being forced wide by the Australian keeper Vince Matassa.
Joachim's 85th-minute strike gave Australia no chance to recover for a second time after they had equalised in the 51st minute through a deflected shot from the striker Ante Milicic. England had gone ahead with a David Unsworth header just before the break. The goal came from a Chris Bart-Williams cross to the far post following a rare, flowing build-up involving Darren Caskey and Joachim.
With Nick Barmby again absent, Joachim carried the burden of being England's lone striker in a formation which seemed unnecessarily cautious for a third-place play-off. 'It is a lot of hard work, but you just keep going,' he said.
BRAZIL: Dida; Bruno, Gelson, Juarez, Marcelinho, Cate, Pereira (Caico, 62 min), Gian, Adriano (Argel, 90 min), Yan, Hermes.
GHANA: Owu; Nimo, I Asare, Gargo, Lamptey, Ahinful, Duah, Akonnor (Boateng, 86 min), Kuffour, Banini, Addo.
Referee: A Cakar (Turkey).
ENGLAND: D Watson (Barnsley); S Watson (Newcastle United), Unsworth (Everton), Myers (Chelsea), Pearce (Chelsea), Hughes (Crewe Alexandra), Bart-Williams (Sheffield Wednesday), Caskey (Tottenham Hotspur), Joachim (Leicester City), Pollock (Middlesbrough), Thompson (Newcastle United). Substitute: Harriott (Oldham Athletic) for Pearce, 56 min.
AUSTRALIA: Matassa; Iocca (Tseknis, 45 min), Holst, Juric, Wingell, Muscat, Carbone, Agostino, Milicic, Tsekenis, Moric (Trpcevski, 51 min).
Referee: M Kathirveloo (Malaysia).