The Red Devils were seemingly on course for a straightforward triumph thanks to Marcel Sabitzer's first-half brace, but a pair of own goals from Tyrell Malacia and Harry Maguire saw the visitors snatch the unlikeliest of stalemates from the jaws of defeat.
Raphael Varane and Lisandro Martinez were also forced off injured for Erik ten Hag's side - the latter appeared to sustain a serious problem in the second half - while Bruno Fernandes picked up a suspension-inducing yellow card on what proved to be a dampening night for one of the tournament favourites.
Without the injured Marcus Rashford against the serial winners of Europe's second-tier competition, Thursday's game had the potential to be a banana skin for the Red Devils, in spite of Sevilla's torrid fortunes in La Liga this season.
However, Ten Hag's side attempted to lay any fears to rest with a blistering first-half display, during which they had the ball in the back of the net after just 27 seconds through Jadon Sancho, but the Englishman had made his run a tad too early and the offside flag went up.
Still coming forward in waves, Antony stung the palm of Bono at his near post in the 13th minute, but the Red Devils would break the deadlock barely 60 seconds later - thanks in no small part to some smart link-up play between Anthony Martial and Sancho on the left.
After Martial had jinked his way past a sea of white shirts and laid the ball off to Sancho, the Englishman drove infield and laid off Fernandes, who picked out Sabitzer with a drilled through ball into the area.
The Bayern Munich loanee controlled Fernandes's fizzed pass expertly, and his strike took a deflection off of Marcao and beyond the reach of Bono, propelling Man United into a deserved lead.
Just seven minutes later, Sabitzer would continue to fill the boots of Rashford admirably with his second of the night, as a Tanguy Nianzou error allowed Martial to burst forward on the break - the Frenchman held the ball up well before picking out the run of Sabitzer, who timed his run to perfection and fired home a low drive into Bono's net.
Los Palanganas' high line was exposed and then some by Man United for their second goal, and Jose Luis Mendilibar's men displayed a distinct lack of pace up top, doing little to offer their travelling fans any hope of a fightback.
One blemish of a near-perfect first half for Man United would be a harsh yellow card for Fernandes for handball - meaning that the playmaker will miss the second leg - and David de Gea had to produce a fine reaction stop to deny Nianzou from a corner in added time before Varane headed clear on the goal-line.
Prior to his vital intervention, Varane had appeared to pick up a knock and was taken off for Maguire at half time, while Sevilla turned to ex-Manchester City winger Jesus Navas for some belated inspiration, the 37-year-old replacing Oliver Torres.
Despite his advancing years, Navas provided a useful outlet down the right for Sevilla, who asked a couple of questions of the Man United backline in the early stages of the second half, albeit without troubling De Gea.
Threatening on the break as ever, Man United were inches away from making it three in the 61st minute thanks to a trademark Antony move - the Brazilian cutting inside and trying to bend one into the top corner with his left foot - but his strike struck the inside of the post and Sevilla cleared the danger.
As a flat second half progressed with little goalmouth action to report on, Sevilla players fell to the turf all over the shop - some legitimately, some not - as their chances of taking a precious goal back to base dwindled.
Navas was one of the Palanganas crop to jar his knee in an awkward slip, but the Spaniard dusted himself down to take advantage of some atrocious defending from Malacia in the 84th minute, ghosting in beyond the Dutchman to keep the ball alive at the back post, and his first-time cross deflected off Malacia and De Gea into the back of the net to give the visitors a slice of hope.
The worried expressions etched across the face of Man United supporters became more apparent when Martinez went down with nobody around him only a couple of minutes later - the disconsolate centre-back had to be carried off the field by Argentina teammates Marcos Acuna and Gonzalo Montiel before being loaded onto a stretcher.
With Man United having already made their allotted changes, the Red Devils would be forced to see out six minutes of added time with 10 men, and the aerially dominant Youssef En-Nesyri would come off the bench to make the Red Devils pay for their second-half passiveness.
Having just had one header kept out by De Gea, the Moroccan marksman rose highest for a second bite at the cherry, and his effort - which was ostensibly travelling wide - struck an oblivious Maguire square in the head and nestled into the far corner to draw Sevilla level.
Ahead of next week's return leg in Seville, a shell-shocked Man United - whose concern will immediately turn to the injuries to Varane and Martinez - travel to Nottingham Forest for Sunday's Premier League tie.
Meanwhile, Sevilla continue their fight against the drop in La Liga when they make the journey to fellow faltering giants Valencia in three days' time.