The Reds’ display was bookended by two poor pieces of defending - conceding within five minutes before giving up a 2-1 lead to cop an equaliser from Carlos Joaquín Correa in the 72nd minute.
Jurgen Klopp’s side came from behind and played some sizzling first-half football, capped by Roberto Firmino and Mohamed Salah goals. But the former also missed a penalty, won by Sadio Mane, while the hosts enjoyed a number of strong chances to extend their lead.
Then came the La Liga side’s sucker punch, and, they arguably finished the stronger, with the Reds ending with 10 men after Joe Gomez was marched in the final seconds.
Philippe Coutinho was summoned off the bench with 14 minutes to go for his Liverpool return.
Elsewhere, there were wins for Premier League outfits Tottenham and Manchester City.
Spurs won a pulsating clash at Wembley against Borussia Dortmund, featuring three superb first-half goals - all within the opening 15 minutes.
Heung-Min Son and Harry Kane sliced the Germans apart down Spurs’ left, with the skipper scoring the decisive third in the second-half.
But Andriy Yarmolenko’s first-half, left-foot curler from way outside the box was the goal of the Matchday, and, the Bundesliga outfit were hard done by with Pierre-Emerick Aubameyang having a goal disallowed that would have made it 2-2.
In Holland, John Stones set the tone for Pep Guardiola’s side with an early goal at Feyenoord, before star strikers Sergio Aguero and Gabriel Jesus got in on the party. Centre-back Stones netted a fourth to inflict a heavy defeat on the Dutch champions, with Australian Brad Jones in goal.
Meanwhile, Cristiano Ronaldo and Sergio Ramos did the damage for Real Madrid as they started their title defence with a 3-0 win over Cyrpriot outfit APOEL.
THURSDAY AEST SCOREBOARD
Maribor 1 Spartak Moscow 1
Liverpool 2 Sevilla 2
Feyenoord 0 Manchester City 4
Shakhtar Donetsk 2 Napooli 1
RB Leipzig 1 Monaco 1
Porto 1 Besiktas 3
Real Madrid 3 APOEL 0
Tottenham Hotspur 3 Borussia Dortmund 1