Both sides started cautiously into the game before Danny Murphy almost gifted Atletico the opening goal after 12 minutes.
The Fulham captain passed right to Sergio Aguero in midfield, who nicely fed Forlan whose left-footed effort hit the far right post.
Fulham goalkeeper Mark Schwarzer parried a dangerous free kick from Jose Antonio Reyes five minutes later and Atletico goalkeeper David de Gea got his first save in the 20th off a long-range effort from the Wales midfielder Davies as Fulham slowly came alive.
Atletico broke the deadlock in the 32nd minute. Reyes sped down the right flank, the ball came to Aguero via Simao, and his attempted shot from the edge of the area was deftly deflected into the low left corner by Forlan for his fifth goal of the competition.
However, the Spanish joy lasted just five minutes.
Zamora appeared to have lost the ball in the Atletico penalty area, but the Cottagers kept the play alive and Davies volleyed home Gera's cross at the far left side.
Forlan had another chance at the end of the half before Fulham enjoyed their best spell early after the break thanks to the lively Davies and Gera.
Tempers flared briefly when Gera made contact with de Gea in the 53rd minute, but the young goalkeeper escaped unharmed and made a super save against a short-range shot from Davies on the hour.
By then Clint Dempsey had replaced the luckless Zamora, becoming the first US player to feature in a European club final. Duff later also went off, in the 84th minute, making way for Erk Nevland.
Caution returned as the end of regulation drew nearer and it was no surprise that the balanced match headed into extra time.
Aguero hit the side-netting in the 105th from almost point blank range as he was under pressure from a defender after great work from Forlan, who then aimed high in the 110th minute.
Atletico finally broke through with four minutes left, with Aguero crossing and Forlan's back-heeler taking a deflection off Brede Hangeland into the net. Forlan ripped off his shirt and was buried by the entire team in celebration.
Gera got a final chance in stoppage time but eventually Atletico celebrated the first of a possible two season titles as they are also in next week's Spanish cup final against Sevilla.