Porto and Braga sealed semi-final wins to set up an all-Portuguese Europa League final in Dublin on 18 May.
Braga overcame a 2-1 first-leg deficit with a narrow 1-0 second-leg victory at home to beat Benfica on away goals.
Porto were overwhelming favourites to progress after their 5-1 first-leg home win over Villarreal, and they confirmed this despite losing 3-2 in Spain.
Falcao set a new record for most goals in a European campaign with his 16th for Porto in this season's competition.
The Colombian's tally beat that of former Tottenham and Germany striker Jurgen Klinsmann, who scored 15 for Bayern Munich as they won this tournament in 1996 when it was known as the Uefa Cup.
Falcao's team may not have won the away leg of their semi-final against Villarreal, but the recently crowned Portuguese champions had already done most of the damage in the first leg at the Estadio do Dragao.
A week ago, Porto boss Andre Villas-Boas saw his side come back from a 1-0 half-time deficit courtesy of five unanswered second-half goals, four of which were scored by the predatory Falcao.
Only three other teams in the history of Uefa club competition ties have recovered from a four-goal first-leg deficit - Leixoes in 1961-62, Partizan Belgrade (against English club QPR) in 1984-85 and Real Madrid in 1985-86.
If Villarreal were to follow suit they would likely need to score early, and they achieved this when Cani poked home Marco Ruben's cross in the 17th minute.
The Spaniards had a superb chance to double their advantage and give themselves a real chance in the tie in the 32nd minute when Santi Cazorla played Giuseppe Rossi in, but the Italy striker fired into the side netting with only goalkeeper Helton to beat.
They would rue this missed opportunity as eight minutes later, Porto essentially decided the tie in their favour when Hulk's shot deflected in off the foot of home defender Mateo Musacchio.
Shortly after half-time, Falcao struck when he was found in the box by Freddy Guarin.
The home side knew the cause was lost, but they managed to reclaim some pride with two further goals to at least win the leg.
Joan Capdevila controlled a cross before firing past Helton to level the score on the night, before Rossi cashed in on a foul by Nicolas Otamendi on Marco Ruben in the area for his 11th goal of the tournament to maintain Villarreal's 100% home record in this season's competition.
The defeat for Porto ends a run of five successive European wins but this will do little to detract from the fact they are now one game away from securing their first European crown since former boss Jose Mourinho led them to Champions League glory in 2004, a year after they had succeeded in the Uefa Cup.
"We were very competent over the two legs," said Porto coach Andre Villas-Boas.
"Villarreal was very aggressive and we kept having to adapt. They made life difficult for us, as we had expected."
Braga were made to work much harder by fellow Portuguese side Benfica to secure what is their first appearance in a major European final.
With Benfica holding a slender 2-1 advantage from the first leg in the Estadio da Luz, this was an understandably tense affair with little to choose between the two, particularly in the opening stages.
However, the home side took their chance in the 18th minute when the visitors failed to deal with Hugo Viana's corner and Custodio was allowed to rise unchallenged to thump home a superb header.
Benfica could have levelled on the night and restored their overall lead shortly after when Fabio Coentrao broke forward and played the ball through for Oscar Cardozo, who then squared the ball first time for Javier Saviola, but his effort came back off the post. The rebound broke to Coentrao but he could do no more than blaze wastefully over.
The visitors went close again on the hour mark when Franco Jara worked space 22 yards out and curled in a shot which just missed the angle of post and bar.
Nicolas Gaitan, Saviola and Alan Kardec all had second-half chances to potentially win the tie for Benfica but a combination of good defending and wastefulness preserved the home side's advantage.
This was Braga's eighth clean sheet in nine European games - a remarkable record that is key to their success in this season's competition.
They will head to Dublin as the underdogs, looking to secure their first silverware since lifting the Portuguese Cup in 1966.
"I think we deserve the final after this great run we've had," said Braga coach Domingos Paciencia. "We've proved we're good enough and we'll be looking to do it again in the final."