Portuguese rivals Braga and Benfica went head-to-head, with the latter leading 2-1 from the first leg.
Custodio gave Braga the lead on away goals with his impressive header.
A header from Custodio gave Braga the lead at home, and an advantage on away goals overall.
Braga players celebrated beating Benfica to reach the Europa League final.
Cani put Villarreal ahead on the night, but they had to overturn a 5-1 deficit.
Hulk levelled the scores with a deflected strike to put Porto 6-2 up on aggregate.
Falcao set a new record when notching his 16th of the Europa League campaign.
Falcao now has the chance to extend his tally in the final in Dublin on May 18.
Joan Capdevila pulled one back for Villarreal with a goal at the far post.
The emotion of an aggregate defeat was too much for Villarreal's Marco Ruben.
Porto have enjoyed a remarkable season, having also won their domestic league.
FC Porto's players and staff celebrated reaching the Europa League final.