The Portuguese champions trailed at the break but an inspired second-half display put Porto on the brink of a place in next month's final in Dublin.
"It's the first time I've scored a 'poker', four goals. A magical night that I will never forget," Falcao said.
"It was a great win. We didn't fall apart after going behind and were able to react rapidly."
Buoyed by the goal, Porto drove forward and went ahead on the hour-mark when Falcao's compatriot Fredy Guarin dribbled past Bruno Soriano on the right wing, cut in to fire a fierce shot against the post and headed in from the rebound.
Falcao added Porto's third in the 67th minute with a tap-in after Hulk led a counter-attack and then the fourth with a diving header from a curling free-kick by Guarin that left the Spanish defence standing.
"He's outstanding, a fantastic striker," said Porto coach Andre Villas Boas, adding that major European clubs who want to lure the Colombian away from Portugal will have to pay a big price tag.
