Liverpool, trailing 1-0 from the first leg, drew level just before the end of the first half through Italian midfielder Alberto Aquilani's low curling shot from inside the box.
A quiet second half set up extra time and the hosts took a 2-0 lead on the night through Yossi Benayoun's angled strike only for Forlan to smash home the ball a few minutes later.
Atletico will meet Fulham in the May 12 final in Hamburg where they will bid to win their first major European trophy since the European Cup Winners' Cup in 1962.
The Spanish side, who face Sevilla in the King's Cup next month, also reached the European Cup final in 1974.
"We have done really well," Atletico coach Quique Sanchez Flores told reporters.
"Today we got stronger as the match went on and over the two legs I think we deserved to go through.I've not known too many better moments."
NEWS:Flores surprised by Atletico run
For Rafa Benitez's Liverpool, Europa League silverware represented a last chance to salvage a dismal season which featured an early Champions League exit and a failed Premier League title challenge.
ATTACKING INTENT
Liverpool started with all the attacking intent Benitez wanted from a side including Steven Gerrard, Aquilani, Ryan Babel and Dirk Kuyt and they forced three corners inside the first two minutes to raise Anfield hopes.
However, the visitors have been dangerous on their travels and as Liverpool lost their passing game Raul Garcia tested goalkeeper Pepe Reina with a dipping shot that was turned around the post.
The hosts' inability to keep the ball up front frustrated the Liverpool fans but with halftime approaching Aquilani came to their rescue, stretching to meet Benayoun's cross and curl home a low shot.
Atletico enjoyed more of the possession after the break but it was Liverpool who almost doubled their lead on 80 minutes when England fullback Glen Johnson skipped past two players before seeing his 20-metre drive tipped over.
Five-times European champions and three-times UEFA Cup winners Liverpool had produced second-leg victories twice already in the competition this season following first-leg defeats and they went ahead early in extra time.
A delightfully-chipped Lucas pass was met by Benayoun who finished well from a tight angle.
Anfield went from raptures to stunned silence shortly afterwards when Jose Antonio Reyes easily beat Johnson to set up first-leg scorer Forlan, who smashed home from five metres for the decisive away goal.
Benitez said: "We were on top for a long time. We lost the game with a late goal but it was a good game.
"It was a pity the way they scored."
