In a pulsating end to three weeks of competition, Neto was the night's hero, scoring the winner -- his second goal of the game -- with penalties looming.
Brazil's talisman Falcao, playing his fourth World Cup, had earlier forced the game into extra time with a late equaliser which stung Spain, who had looked set for victory after two second-half strikes from Aicardo and Torras.
Facing defeat the defending champions launched a barrage of attacks culminating in Falcao's equaliser with minutes of normal time on the clock.
The European champions were distraught at the end of a match they dominated for long periods with Neto's last-gasp goal condemning the Spaniards to a second final defeat to Brazil on the spin.
Brazil won the 2008 edition on penalties after another thrilling 2-2 draw in normal time.
The champion's free-scoring streak, which saw 42 goals in five games propel them to the final, appeared to have deserted them at the wrong time.
But Falcao's equaliser sparked an extra-time surge against the deflated Spaniards in a match to delight fans of the indoor game.
Sunday night's climax to nearly three weeks of competition was the fourth time the two sides have competed for the world title.
They are also the only two sides to win the World Cup since it began in 1989.
Italy meanwhile took bronze with a one-sided 3-0 win over tournament surprise packages Colombia, whose outstanding goalkeeper was sent off early in the second half for handling outside the area.
Itay's winning coach Roberto Menichelli hailed his side's strong showing in Bangkok saying it was "a source of great pride... that we have finished as the second-ranked European team after Spain."
The fiercely-contested knock-out stages have finally taken attention away from controversy that dogged Thailand's preparation for the event.
Football's governing body FIFA forced Thailand to move the knockout stages -- including Sunday's final -- from a new $40 million stadium after construction delays meant the venue failed safety tests.