Jürgen Klopp's side looked set to cruise to a victory that would have seen them through as group winners after a first-half double from Roberto Firmino and a further strike from Sadio Mane gave them a three-goal lead at the break.
However, Wissam Ben Yedder's quickfire brace after the restart made for a nervous final 30 minutes at the Ramon Sanchez Pizjuan.
And the hosts levelled things up in the 92nd minute as Guido Pizarro pounced to smash the ball home after the Reds had failed to clear a corner.
Liverpool now go into next month's Anfield meeting with Spartak Moscow knowing that a win would see them into the last 16 courtesy of a first-placed finish.
The key points…
- Firmino scores either side of Mane goal in first half
- Ben Yedder brace in second half gives Sevilla hope
- Pizarro hits last-minute equaliser
- Reds will win group with Spartak Moscow victory
The team news…
Klopp elected to make just two changes from the weekend's convincing win over Southampton as his team turned their attentions to Europe once again.
Joe Gomez came in at right-back for Trent Alexander-Arnold, while Loris Karius returned for Champions League action in place of Simon Mignolet in goal.
The first half...
A dazzling light show prior to kick-off only added to the white hot atmosphere in Seville but the Reds quickly set about doing their bit to silence the home fans.
Fewer than two minutes had elapsed when a flicked on corner landed to Firmino at the back post and he smashed home emphatically to give the visitors the lead.
To their credit, Sevilla brushed off that early blow quickly and began to assert themselves as the half wore on.
And, but for the fingertips of Loris Karius, they would have been level in the 19th minute.
The German did brilliantly to tip Nolito's shot onto the post after the forward had evaded Joe Gomez in the box following a quick break.
However, the No.1 was not needed just a minute later when Ben Yedder burst clear, the striker mercifully dragging his shot inches wide of the upright.
Those misses were then immediately punished by Mane, the Senegalese stooping to head in yet another flicked on corner, much to the delight of the away supporters who may have been biting their nails moments earlier.
And the Travelling Kop truly were in dreamland on the half-hour mark as Firmino tapped into an open net after Mane had been thwarted inside the box.
Things could have been even better for the Reds at the break had Firmino and Salah finished off one-on-one chances either side of the second and third goals, but Klopp could have few complaints with how his team had fared.
The second half...
Sevilla made the brighter start to the second half as they looked to make amends for a one-sided opening 45 minutes and quickly gave the home fans something to cheer as they looked for a turnaround.
The hosts gained momentum when Ben Yedder nipped in front of two Liverpool defenders to nod a header past Karius six minutes after the restart, and subsequently laid siege to the Reds goal.
That pressure paid off on the hour mark when an Alberto Moreno trip gave Sevilla a penalty, which Ben Yedder converted twice after being forced to retake due to encroachment.
In a bid to help settle his side down, Klopp called for James Milner and Emre Can from the bench, the pair replacing Moreno and Philippe Coutinho respectively.
The changes had the desired effect as Sevilla struggled to get through the middle of the park from that point onward, while Liverpool mustered a huge chance of their own on the break only for Can to be denied by Sergio Rico.
But they were hit with a sucker punch just seconds from the final whistle as the ball fell fortuitously in the box for Pizarro to poke home and level things up.
The stats...