Roberto Firmino scored twice - the Brazilian breaking the deadlock inside two minutes - and Sadio Mane also found the net as Jurgen Klopp's side coasted into 3-0 half-time lead in the battle between the top two in Group E.
However, a second-half meltdown, triggered by two mistakes from former Sevilla defender Alberto Moreno, saw Liverpool let a seemingly certain victory slip from their grasp.
Wissam Ben Yedder struck twice after the break, heading home a free-kick before converting a penalty, as Sevilla fought back valiantly against the same opponents they defeated in the 2016 Europa League final.
The visitors looked set to hold firm through to the final whistle until Guido Pizarro popped up with an injury-time equaliser, leaving the group still in the balance with one more round of games to play.
With Maribor grabbing a late equaliser against Spartak Moscow in the early kick-off, Liverpool's task was clear - win and they would not only be in the knockout stages for the first time since the 2008-09 season but also assured of topping the table.
Their task was meant to be a tough one, considering their opponents had not lost in front of their own fans since a 3-1 reverse against Juventus at the same stage of the competition last year, yet they stunned Sevilla by racing into a 3-0 first-half lead.
They scored two almost-identical goals from left-wing corners delivered by Philippe Coutinho, Firmino on hand at the back post to turn home Georginio Wijnaldum's flick-on and break the deadlock after just 88 seconds.
The Brazilian was also heavily involved in Liverpool's second, this time getting his head to Coutinho's out-swinging delivery to tee up the late-arriving Mane.
Sevilla, who had seen Nolito hit a post and Ben Yedder shoot narrowly wide when the score was still 1-0, were undone by a long ball for Firmino's second of the game.
Dejan Lovren's punt out of defence saw Mane burst clear down the left and although Sergio Rico saved his attempt, the grateful Firmino was on hand to tap the rebound into an unguarded net.
3 - Liverpool have let a three-goal lead slip in a competitive match for the first time since May 2014 against Crystal Palace in the Premier League (also 3-3). Comeback.— OptaJoe (@OptaJoe) November 21, 2017
At that stage, Liverpool seemed to be coasting. However, the team who played with pace and purpose before the break failed to make a re-appearance for the second half, leading to an uncomfortable conclusion.
The hosts grabbed the early goal they needed to raise hopes of an unlikely recovery, Moreno's needless foul out wide enabling Ben Yedder to nod in the influential Ever Banega's right-wing free-kick.
Liverpool's left-back was also guilty of giving away the spot-kick for Sevilla's second, compounding his initial error of letting the ball slip through his legs by tripping Ben Yedder, who sent Loris Karius the wrong way twice after his initial attempt was ruled out for encroachment.
Klopp reacted to the onslaught by taking the shell-shocked Moreno out of the firing line, sending on James Milner to play in a position he occupied so regularly last season.
The change appeared to help solidify a shaky defence until Pizarro pounced from a corner in added time, turning home an equaliser that means Liverpool have to wait until they host Spartak to secure a place in the next round.
Key Opta stats:
- The Reds have scored the same number of goals in their last three Champions League games (13) as they did in their previous 14 matches in the competition combined.
- In the two games between these sides in the Champions League this season, Liverpool have attempted more than twice as many shots as Sevilla (37 v 18) but scored the same number of goals (5).
- This result means that Premier League clubs are now unbeaten in six successive Champions League matches against teams from La Liga (W2 D4 L0).
- Roberto Firmino has now been involved in seven goals in five Champions League appearances this season for Liverpool (five goals, two assists).
- Roberto Firmino's opening goal came after 01:28 – their second-fastest goal in Champions League history; one second slower than Florent Sinama-Pongolle's in September 2005 at Real Betis (01:27).