The prolific Colombian struck gold once more, scoring a brilliant brace in the first half which, added to a fine breakaway goal from Diego, sealed the trophy for the capital outfit
The Colombian striker, who scored the winner for former club Porto in last season's final, produced two superb individual efforts in the first half alongside an equally fantastic clincher from Diego to ensure that Atletico regained the trophy that they last won in 2010.
Falcao's strikes took his tally in the competition to 12, confirming him as the tournament's top scorer for the second campaign running, as Bilbao never found a way back into the match, despite laying siege to the Atletico goal for large periods in the second half.
Atletico were on the front foot straight from kick off, impressing with some incisive link-up play in the attacking third. When the opener arrived after seven minutes, though, it was all down to the brilliance of one man.
The ball was played to Falcao on the right side of the box, who showed delicate footwork to manufacture an inch of space and bend a sumptuous effort past Gorka Iraizoz into the top corner.
Bilbao were slow to respond to the setback and were faced with further danger when Diego dragged a shot wide from the edge of the area.
Atletico’s threat diminished shortly after, however, as they seemed content to sit back and invite Bilbao to take the game to them; an offer which the Basque outfit accepted.
Fernando Llorente sliced a close-range volley off target, before Iker Muniain forced Thibaut Courtois into a smart save with a low drive from just outside the box, as Marcelo Bielsa’s men began to establish a foothold in the game.
But just when they looked to be turning the match back into their favour, they were taken apart by another moment of quality from Falcao on 34 minutes.
Arda Turan’s pass found the Colombian in a great position, and his twists and turns left marker Jon Aurtenetxe on his backside before blasting home from close range for his 29th Europa League goal in 29 games.
The momentum was now with Atletico, and Falcao nearly rounded off his hat-trick on the stroke of half time after cutting in from the left side, but this time his finish deserted him.
Bilbao came storming out of the break and a strong run and cross from Muniain was turned away at the last by Diego Godin with Llorente lurking for the tap-in.
Inigo Perez’s tricky cross-cum-shot forced Courtois to tip over, and as the game crossed the hour mark, Bilbao slowly began to set up shop deep in the Atletico half.
Two chances went begging for Marcelo Biesla’s men, with both Andoni Iraola and Oscar De Marcos firing over the bar from positions where they really should have hit the target.
Susaeta went even closer with just over 10 minutes to go with a low drive from the right that Courtois did well to beat away.
But with large numbers camped in the opposition half, Bilbao were always vulnerable on the counter. Falcao had another chance to complete his treble after breaking free in the 80th minute but could only strike the post with Iraizoz beaten.
Bilbao were caught out on the break again five minutes before the end, and this time Atletico made them pay. Collecting the ball a fair distance from goal, Diego left two defenders in his dust before stroking a fine finish across the goalkeeper to put the match beyond any doubt
Ibai produced a late stunner that hit the woodwork, but it was of little consequence, as Bilbao’s European adventure all too literally ended in tears, with Atletico emerging as Europa League champions for the second time in two years.