The Reds took to the Estadio Ramon Sanchez Pizjuan safe in the knowledge that a victory over the Liga outfit would secure top spot in Group E.
And Sadio Mane made it 2-0 with a carbon copy of the Brazilian’s goal 20 minutes later, before the two combined for Firmino’s second on the half-hour mark.
This saw the Reds head into half-time with a commanding lead, and one foot in the last 16 of Europe’s top-tier tournament.
The first saw Wissam Ben Yedder head home Ever Banega’s free-kick, before the Frenchman stepped up to fire a penalty beyond Loris Karius to make it 3-2.
Liverpool looked to hold on as Klopp made a series of changes in an effort to shore things up.
But with Sevilla winning a corner late on, the loose ball fell to Guido Pizarro, with the Argentine midfielder smashing home to seal a remarkable draw.
The Reds now need at least a point from their final group game at home to Spartak Moscow on December 6 in order to reach the next stage.