Forlan got his second goal of the game when he flicked Sergio Aguero's cross under his standing leg, the ball rolling past goalkeeper Mark Schwarzer via a deflection off Fulham defender Brede Hangeland.
Man-of-the-match Forlan, who also hit the post and put Atletico ahead in the 32nd minute, was the only Atletico player not to celebrate at the final whistle as the club won its first trophy since the Spanish league and cup double in 1996.
The Uruguay international instead shook hands with the exhausted Fulham players, who had been trying to clinch the west London club's first major title.
Forlan's goals earned Atletico only its third win from 15 European games this season but still gave his club the distinction of being the first to win the title in its latest guise.
The tournament was known as the UEFA Cup until it was revamped and renamed for this season at the behest of UEFA president Michel Platini.
Forlan scored his first goal by redirecting a mis-hit shot by Aguero, but Fulham equalised just five minutes later through Simon Davies' fierce right-foot volley.
Aguero was dangerous throughout for the nine-time Spanish champions and the Argentina international almost scored himself, shooting into the sidenetting, before setting up Forlan for the winner.
Striker Bobby Zamora helped set up Fulham's equalizer but was forced from the field early in the second half with the Achilles' injury that kept him out of England's initial World Cup squad.
Fulham began to struggle up front without a focal point for its attack, but it almost withstood all of the nine-time Spanish champions' best efforts - even after Atletico coach Quique Sanchez Flores replaced tiring wingers Juan Antonio Reyes and Simao Sabrosa.
Zamora's 55th-minute exit gave Clint Dempsey the opportunity to become the first American player to appear in a European final, but the United States striker struggled to make an impact.
With Erik Nevland coming on up front in place of Damien Duff, who only played after a late recovery from a leg injury, Fulham lacked a cutting edge despite some neat play in midfield.
Atletico's central defence of Mariano Pernia and Alvaro Dominguez was mostly untroubled for the last hour.
