The Portuguese side finished level with Sevilla on aggregate, 2-2, but advance to the next round courtesy of the two away goals they scored in the first leg three weeks ago.
Substitute striker Luis Fabiano scored the only goal of a thrilling encounter in the 71st minute, before both sides were reduced to 10 men in the final 20 minutes.
Porto's Alvaro Pereira was shown a straight red two minutes after Sevilla’s goal for a two-footed lunge, before Alexis was shown a second yellow card for the visitors four minutes later, after dragging Porto striker Hulk down by the shirt.
The visitors were lucky to still have 10 men on the pitch by the final whistle, however, after Fernando Navarro - shown a yellow card after just 13 minutes - survived despite a rash of ill-judged challenges, and Diego Perotti got away with a full-blown punch in an ugly off the ball incident after 67 minutes.
Porto welcomed Sevilla to the Dragao with one foot already in the last-16, thanks to their last gasp 2-1 victory in the first leg.
Sevilla had bossed that match, but Fredy Guarin’s 85th-minute winner handed the Portuguese SuperLiga leaders two ultimately pivotal away goals – leaving Sevilla needing at least two goals in Portugal to have any hope of survival in Europe’s second competition.
The visitors also had to make do without first choice goalkeeper Andres Palop and defender Martin Caceres – both sidelined through injury – while former Porto striker Luis Fabiano was dropped to the bench after failing to find the back of the net in the first leg.
Sevilla started brightly, with Freddy Kanoute firing narrowly wide just two minutes into his 250th appearance for the Andalusians.
However, the chance proved to be Gregorio Manzano’s side’s only real goal-scoring opportunity of the half, as Porto began to show the form that has seen them win eight of their nine Europa League matches this season.
Fernando Bulluschi fired an immaculate volley a yard wide of the right post from 30 yards after 20 minutes, before full-back Perreira forced a fabulous diving save from Javi Varas nine minutes later from even further out.
With Porto continuing to press forwards – and Sevilla becoming increasingly reliant on robust defensive tactics to batter the hosts’ attacks into submission - Andre Villas-Boas’s side were denied a first-half win by the width of the crossbar in the 33rd minute.
The lively Falcao met Varela’s pin-point cross with a bullet header from 15 yards out, angling the ball clear of Varas’s reach but seeing it cannon back off the corner of the goal frame.
The 25-year-old Colombian’s shameful dive in the area straight from the rebound was less impressive, but English referee Howard Webb was unmoved by Falcao’s pleas for a penalty.
An ill-tempered first half - in which Sevilla defenders Alexis and Navarro were both lucky to receive just one yellow card apiece – ended in further acrimony as the referee’s whistle blew, with Hulk and Didier Zokora nearly coming to blows in the middle of the pitch.
Both side's exchanged chances at the start of the second half - Belluschi volleying over the bar in the 51st minute and Perotti firing just wide of Helton's right-hand post three minutes later - before Manzano finally threw caution to the wind and introduced Fabiano from the bench, in exchange for full-back Sergio Sanchez.
Sevilla's triple-pronged attack of Fabiano, Kanoute, and Alvaro Negredo instantly gave the hosts a more obvious attacking edge, but also left them repeatedly exposed at the back - something Porto exploited repeatedly in the run up to Sevilla's goal.
First Falcao forced a tremendous sliding block from Fazio in the 58th-minute, before Hulk forced a fine save from Varas three minutes later.
Joao Moutinho fired narrowly wide in the 65th, before Hulk missed a gilt-edged chance to put Porto ahead - firing wide of the right post from a one-on-one with Varas in the 70th minute.
Sevilla dealt with the punches, before Fabiano scored his winning goal against the run of play just one minute after Hulk's miss.
The Brazilian drove into the area through the middle of Porto's defence, before slamming the ball expertly past Helton.
After the two red cards, the game reached a fever pitch that remained until the final whistle - both side's breaking through on goal almost at will but continually failing to find the target.
Hulk was particularly culpable for Porto - forcing three fine saves from Varas - but Kanoute and Negredo both came close to stealing what would've been a tie-winning goal for the visitors - Negredo seeing a close-range shot blocked behind for a corner in the 81st minute and Kanoute heading marginally wide from the resulting corner.
However, Sevilla ultimately failed to make Porto pay for their profligacy, and the Portuguese leaders breathed a sigh of relief as the final whistle confirmed their progression to the next round.