Substitute Luis Fabiano's 71st-minute goal gave Sevilla a 1-0 win at Porto on Wednesday but the Portuguese club advanced to the last 16 of the Europa League on the away goal rule.
Porto won 2-1 in Spain last week.
Sevilla brought on Brazilian striker Fabiano in the 55th, taking off defender Sergio Sanchez in a bid to break the deadlock. Fabiano picked up a pass from Alvaro Negredo, muscled past Fernando and hit a low shot into the far corner.
Porto defender Alvaro Pereira was sent off for a dangerous tackle two minutes after Fabiano's strike but then Sevilla's Alexis was shown a second yellow card to leave both teams with 10 men.
Porto had most of the chances in a lively game at the Stadium of the Dragon and appeared to be heading comfortably for the next round before Fabiano struck to set up a nervous finish.
Sevilla goalkeeper Javi Varas made a half-dozen impressive saves to deny Porto, while Falcao headed against the woodwork.
Sevilla started the encounter strongly and Frederic Kanoute, who got his team's goal in Spain, hit a curling short just wide in the third minute.
But from then on it was mostly one-way traffic as Fernando Belluschi and Alvaro Pereira tested Varas.