It was Atletico's first major trophy since winning a domestic League and Cup double in 1996, but for Fulham and manager Roy Hodgson it was a heartbreaking end to an epic run which started in July last year and ended with defeat in their 19th match in the competition.
"You always enjoy goals like that, especially given the timing," Forlan said in a television interview.
VIDEO:Watch Forlan's late winner
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Forlan, who also scored the winner in the semi-final win over Liverpool, gave the Spaniards the lead in the 32nd minute when he side-footed home after a mishit pass from Argentine forward Sergio Aguero.
Simon Davies levelled five minutes later with a superbly taken volley at the far post for the English Premier League team, who have never won a major trophy.
The game fell away until the South Americans paired up again with four minutes left. Aguero chased a seemingly lost ball, beat his marker and produced a low cross which Forlan flicked into the net from six metres.
"I couldn't be more proud of the players for this season and this performance tonight," Hodgson said.
"This performance summed up what we are at Fulham. All season we have been performing against the odds."
It was a dramatic finale to a game which started well but fell away in the second half.
Forlan was close to an early goal for Atletico when he shot against the bottom of the post after a counter-attack led by Aguero.
Jose Antonio Reyes then saw a dipping free kick turned away to Mark Schwarzer as the Spanish side made a bright start.
The Spaniards went ahead in the 32nd minute when a neat exchange of passes ended with Aguero mishitting a shot which fell perfectly for Forlan to sidefoot home from 12 metres
Atletico's lead lasted only five minutes before Davies, who had tested David de Gea with a 20-metre shot just before Atletico's goal, volleyed home Zoltan Gera's chipped pass for a clinical equaliser.
Forlan nearly put Atletico back in front before halftime with a skidding shot which Schwarzer turned away with difficulty.
Fulham pushed forward after halftime, teenager De Gea diving bravely at the feet of Davies to foil a breakaway and then making a superb reflex save from the Fulham scorer's 12-metre drive.
The game deteriorated into a nervous scrap with Forlan offering a few bright interludes.
The Uruguayan set up an excellent chance at the end of the first period of extra-time when he burst down the left and sent the ball into the goalmouth, but Atletico could not find a finish.
The breakthrough came near the end when Aguero chased a long ball down the left, outfoxed his marker and provided a low cross for Forlan to score.
Hundreds of ecstatic Atletico fans had already gathered at the Neptune fountain in central Madrid where the club's titles are traditionally celebrated.
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