The Reds' first outing in the competition since 2014 got off to a nightmare start when they fell behind to a Wissam Ben Yedder strike after just five minutes, but goals from Roberto Firmino and Mohamed Salah turned the game around before half time and ensured that the hosts went into the break ahead.
It should have been ever better for the five-time European champions when they were awarded a penalty, but Firmino hit the post from 12 yards and that proved to be one of many costly misses as Joaquin Correa earned a point for the visitors with just under 20 minutes remaining
Jurgen Klopp opted to leave fit-again Philippe Coutinho out of his starting lineup for the match as his side looked to bounce back from their 5-0 defeat to Manchester City on Saturday, and they made a bright start with Emre Can drawing a stop from Sergio Rico inside the first minute.
It was the visitors who made the early breakthrough, though, as Liverpool's defensive frailties came back to haunt them again after just five minutes when Ben Yedder continued his fine goalscoring form with a simple tap-in following a move littered with Liverpool errors.
Can, Joe Gomez and Dejan Lovren were all guilty of failing to deal with the danger, with the latter allowing a low cross from the left to squirm under his boot and reach Ben Yedder, who was left with an easy finish to make it four goals in his last five appearances.
Liverpool were quick to respond to the early setback, though, with Can seeing one drive deflect narrowly wide before Salah and Sadio Mane teamed up to force Rico into a smart reaction stop down to his left.
Firmino rippled the top of the netting with a header from a corner moments later as Liverpool continued to apply the pressure, and it was the Brazilian who levelled things up for Klopp's side midway through the first half.
Alberto Moreno, who stood out against his former club, exchanged a one-two with Jordan Henderson down the left channel before playing a low pass into the box that left Firmino with the simplest of finishes from close range.
It was almost two goals in as many minutes when Liverpool quickly got on the front foot again, but Can was unable to apply the finishing touch to a lightning counter-attack when he rolled an effort narrowly wide of the far post with only the keeper to beat.
The hosts continued to look the more likely of the two teams as Sevilla struggled to deal with their attacking pace, but Liverpool's second came via fortuitous means when Salah robbed Steven N'Zonzi of possession before seeing a long-range drive deflect off Simon Kjaer and loop past the helpless keeper.
It should have been 3-1 with just a couple of minutes to go until half time when Liverpool were awarded a penalty after Nicolas Pareja first handled the ball in the area before dragging Mane to ground after the winger had skipped away from him. Firmino stepped up to take the spot kick, but he saw his effort come back off the post having sent Rico the wrong way.
Liverpool kept coming, though, and Moreno almost got his own name on the scoresheet with the final action before half time when he was played in by Firmino before being denied by another good stop from Rico.
Clear-cut chances were hard to come by for either side in the opening stages of the second half, but Liverpool continued to look the more dangerous and Salah came close twice before Firmino flashed an effort wide of the target.
Mane then curled one of his own just over the crossbar before Georginio Wijnaldum tested Rico from outside the area, but Liverpool were made to rue their missed opportunities when Sevilla scored the equaliser against the run of play with less than 20 minutes remaining.
Klopp quickly turned to Coutinho off the bench in search of a winner as the Brazilian playmaker made his first club appearance of the season having seen his desired summer switch to Barcelona denied by Liverpool.
Neither Coutinho nor fellow subs Daniel Sturridge and Alex Oxlade-Chamberlain could make the difference late on, though, and it was Sevilla who came closest to winning it in stoppage time when Muriel shrugged off Gomez only to slide his finish wide of the target.
There was further disappointment for the hosts in the final minute of stoppage time too as Gomez picked up a second yellow card late on, earning his marching orders and a suspension for the trip to face Spartak Moscow on matchday two.
All four sides in Group E now sit level on one point after the first game, with Maribor - who take on Sevilla next time out - drawing 1-1 with Spartak in their match.