Portuguese rivals Benfica and Porto are on course to meet in the Europa League final in Dublin after securing semi-final first-leg victories.
Falcao scored four goals as Porto came back from a goal down to secure a 5-1 home win over Spanish side Villarreal.
The other, all-Portuguese semi-final is more finely balanced after Benfica beat Braga 2-1 in the Estadio da Luz.
The return legs will be played on Thursday 5 May, with the final taking place at Lansdowne Road on 18 May.
Porto's victory came courtesy of a stunning comeback after Cani had given Villarreal a 1-0 half-time lead.
The Spanish side had looked dangerous a number of times throughout the first half, breaking through the home side's high defensive line.
And in the 45th minute the visitors took advantage when Nilmar was given space on the right to cross to the near post where Cani ghosted in to glance a header past home keeper Helton.
Villarreal had a superb chance to double their advantage early in the second half when Santi Cazorla was fed in down the inside-left channel, but instead of shooting he crossed aimlessly into the centre and Porto were able to clear.
The Spaniards were left ruing that miss as minutes later Falcao ran clear and was sent tumbling by away keeper Diego Lopez inside the box for a penalty.
The striker picked himself up and sent the keeper the wrong way to equalise.
The home side were now completely transformed and attacked with fluency. Just after the hour they were rewarded when Falcao's fellow Colombian Fredy Guarin headed in after Lopez had saved his initial angled shot.
Six minutes later, Falcao stabbed in Hulk's cross to make it 3-1.
With Porto now completely in control the striker completed his hat-trick with a diving header from a free-kick and then scored his fourth, and his side's fifth, with another header, this time from a corner, in the final minute.
As a result of his four goals, Falcao has now scored 15 goals in this season's Europa League, making him the top scorer in the competition.
Andre Villas-Boas' side have now won 13 consecutive matches, during which they claimed their 25th domestic league title and progressed through to the Portuguese cup final.
Benfica's victory over Braga was less emphatic but no less deserved as the home side largely dominated the all-Portuguese semi-final.
Jorge Jesus' side had the ball in the net early on in the match through Oscar Cardozo but unfortunately for them the Paraguayan striker was ruled to be offside when reacting to Javi Garcia's saved header.
Cardozo would waste two further chances in the first half, firstly chipping over and then hitting a post with a shot after holding off Braga defender Paulao.
However, early in the second half, the home side broke the deadlock when Maxi Pereira tricked his way past Alan and into the area and while Cardozo headed his floated cross against the post, the rebound fell perfectly for Jardel to poke home.
The lead would last only three minutes, though, as the visitors struck back for what could prove to be a valuable away goal.
Hugo Viana whipped in a free-kick and Vandinho was on hand to expertly divert a header past home keeper Roberto.
Both were well-crafted goals, but paled in comparison to Cardozo's winner a minute before the hour mark.
Alan felled Carlos Martins on the edge of the area and from the resulting free-kick Cardozo powered a shot over the wall and in.
The goal ensured Benfica will take a lead to their rivals in seven days' time, but they will be without playmaker Pablo Aimar after he picked up a booking that leads to his suspension for the second leg.
Braga will be without goalscorer Vandinho, who will also be suspended after picking up a yellow card.