Porto's compatriots Benfica, attempting to reach their first European semi-final for 17 years, thrashed PSV Eindhoven 4-1 with all their goals coming from Argentines - two from Eduardo Salvio and one each from Pablo Aimar and Javier Saviola.
Two goals from Brazil striker Nilmar helped Villarreal to a 5-1 win over Dutch league leaders Twente Enschede as 19 goals were scored on the night - one more than the total netted in this week's Champions League last eight first leg matches.
Dynamo Kiev were held to a 1-1 draw at home to Braga, Portugal's third representatives and conquerors of Liverpool in the last 16, in the other tie with Andriy Shevchenko sent off just 15 minutes after coming on as a half-time substitute.
The former AC Milan and Chelsea player was booked twice in eight minutes, the second for playing on after the whistle had gone for offside.
Porto and Benfica, who met on Sunday with Porto winning 2-1 to clinch the Portuguese title in the stadium of their great rivals, both started with eight South American players in their lineups and their matches unfolded in near identical style.
Colombia striker Falcao, whose second Europa League hat-trick made him top scorer in this season's competition with 10, opened the scoring for Porto in the 37th minute, sweeping home Alvaro Pereira's cross.
Silvestre Varela was the only Portuguese player to get on the scoresheet in any match when he volleyed in Falcao's pass in the 65th and Brazilian defender Maicon headed the third five minutes later.
Kirill Kombarov pulled one back in the 70th only for Falcao to add two more in the last six minutes.
"I think this is one I will remember forever," Falcao told reporters. "Even though we clinched the title on Sunday, we did not sway from the objective which is to go ahead in this competition to the final."
EINDHOVEN OUTCLASSED
Benfica utterly outclassed PSV Eindhoven, helped by two Argentine names from the past and one prospect for the future, in a repeat of the 1988 European Cup final which the Dutch won on penalties.
Former international Aimar swept home the opener in the 37th minute and 20-year-old Salvio added the second with a clever flick from Fabio Coentrao's cross on the stroke of halftime.
The Argentine influence was clearly visible in Benfica's quick passing and clever flicks and Salvio added a superb third in the 53rd, beating two defenders before rolling the ball into the far corner.
PSV's Zakaria Labyad pulled one back with 10 minutes left after goalkeeper Roberto fumbled a cross but former Barcelona and Argentina forward Saviola fired home a superbly-taken fourth goal in time added on.
Spain's last representatives Villarreal were 3-0 up against twente by the break with goals from Carlos Marchena, Borja Valero and a Nilmar header in first-half injury-time.
Italian Giuseppe Rossi curled in his ninth of this season's
