Coach Luis Castro said in the build-up that Porto's status as favourites in almost every game they play has hampered them this season - the reigning Primeira Liga champions sit third in their domestic division, 15 points adrift of leaders Benfica - but they put in a commanding display at Estadio do Dragao on Thursday.
After dominating the early stages, Porto finally took the lead just after the half-hour mark as captain Eliaquim Mangala powered a diving header in from an audacious Ricardo Quaresma cross.
Castro's side almost went into the break with a two-goal lead, but Steven Defour's effort from distance was nudged on to the post by former Porto keeper Beto to keep Sevilla in the game.
The away side should have levelled late on as Kevin Gameiro skewed wide from close range, and although Porto will be without Fernando following his late dismissal for a second bookable offence, they take a narrow advantage to Seville for next week's second leg.
With Sunday's 2-1 defeat to Nacional typifying Porto's faltering domestic campaign, Sevilla - who had won six league games in a row before Saturday's 1-0 loss at Celta Vigo - arrived in Portugal looking to compound their misery in the Europa League.
The hosts enjoyed an encouraging start, however, keeping Sevilla camped in their own penalty area for long periods, but the Spaniards' defence stood firm despite a flurry of Porto corners.
Unai Emery's team weathered the storm and almost broke the deadlock with their first chance in the 27th minute as Vicente Iborra flicked on Ivan Rakitic's left-wing free-kick, only for home keeper Fabiano to block the header.
The visitors were made to rue that miss four minutes later, though.
Quaresma - who scored in Porto’s 3-2 aggregate win over Napoli in the last round - delivered a brilliant cross with the outside of his right foot and Mangala directed it into the goal with a ferocious diving header.
Beto did well to deny the hosts a second in the 45th minute, as he acrobatically tipped Defour's long-range effort on to his left post.
Sevilla appeared more willing to venture forward in the second half and they nearly capitalised on an error by Mangala in the 49th minute, as Coke charged down his clearance before seeing a shot deflected wide from an acute angle.
Goalscoring chances were more infrequent than the first half, but Porto striker Jackson Martinez did go close with just over an hour gone with a half-volley that flashed over the bar from close range.
And with 15 minutes to go, Sevilla substitute Gameiro missed a massive chance to equalise as he pounced on a rebound, only to scuff his effort and miss the target.
Porto's position was put in jeopardy in the 87th minute as Fernando picked up his second yellow card for a foul on Gameiro, but Queresma almost extended their lead in injury time as he struck a half-volley onto the post after his initial free-kick had been blocked by the wall.
