Goals by Cani, Joan Capdevila and a Giuseppe Rossi penalty guided the Spanish side to victory with Falcao and Hulk on target for the Portuguese, who held a 5-1 advantage from the first leg.
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Falcao's goal saw him set a new UEFA Cup goalscoring record in a single season with his haul of 16 eclipsing Jurgen Klinsmann's efforts in 1995/96.
Villarreal had been blown away by the Portuguese champions last week where, despite Cani giving them the lead, they had conceded five goals with Falcao grabbing four.
It was imperative the hosts made a good start as they looked for an improbable comeback and they played from the off with a ferocious tempo.
Nilmar whipped in a second-minute cross from the right forcing Porto goalkeeper Helton to come off his line and punch away before the free-scoring Portuguese almost went further ahead, Cristian Rodriguez flashing a shot from the left across goal.
Marco Ruben then put a header over the bar for the hosts before Cani had a seventh-minute chance to reduce the arrears but struck the ball to the centre of the goal enabling Helton to palm the ball away.
Rossi just failed to connect with Ruben's delivery in front of goal before Villarreal got a potential lifeline, Ruben beating the offside trap and putting the ball across to Cani who had got ahead of his marker and slotted the ball into the bottom right-hand corner.
After the initial excitement there were few clear-cut openings for either side before Rossi shot into the side-netting rather than picking out Cani in front of goal on the half-hour.
However, any hopes the Spanish side had of a comeback evaporated when Porto levelled in cruel circumstances for the hosts.
Hulk went to shoot from 25 yards and, although his shot was on target, it hit Mateo Musacchio and looped over helpless goalkeeper Diego Lopez.
Hulk could have extended Porto's lead on the night in first-half injury time but Lopez saved his shot with his legs while Nilmar went inches wide just before the whistle.
It was all over two minutes after half-time when Falcao hit his 16th goal of this year's Europa League campaign, trapping and slotting home Fredy Guarin's pass from the left.
Guarin then hit the bar with a free-kick before Nilmar missed a good chance, failing to shoot on target when well-placed.
Capdevila took advantage of poor Porto defending when he collected a cross at the far post, brought the ball down and volleyed home with a quarter of an hour left.
Three minutes later the hosts were awarded a penalty when Nicolas Otamendi brought down Ruben, Rossi coolly lifting the ball home.