Having drawn against both Sevilla and Spartak Moscow, the Reds need six points from six in their double header against the reigning Slovenian champions - who they face again at Anfield in a fortnight - to ignite their campaign and maintain any hope of topping Group E.
And Liverpool's season as a whole requires victory on Tuesday night, too. Jürgen Klopp's side have only won one of their last eight games in all competitions, drawing five.
Familiar failings continue to let the Merseyside outfit down, their wasteful finishing and error-prone defending costing them in both of their European outings this term.
Liverpool have not won an away game in the Champions League since November 2009, when they beat Hungarian side Debreceni VSC.
That win was not enough to spare them from demotion to the Europa League and a similar outcome from this year - a possible but unlikely circumstance - would be represent a massive underachievement.
Even two points from their opening two points can be viewed as a below-par performance, with Liverpool backed as favourites to win the group with relative ease given that they avoided some tough teams in the draw having been in Pot 3.
Back-to-back wins against Maribor would undoubtedly give Liverpool's continental campaign a rosier outlook, but they will likely face the challenge of an ultra-defensive outfit once more.
Klopp's men have continually struggled to break down opponents that condense the space and prevent them the chances to get in behind, even in spite of their attacking quality.
Darko Milanič's minnows are expected to set up with a 4-4-2/4-4-1-1 formation at the Stadion Ljudski vrt (People's Garden) but will hope for a more resilient defensive performance than their 3-0 defeat at Sevilla last month.
Vijoličasti (The Purple) mustered only a single shot on target and were comfortably second-best for almost all of the 90 minutes in Spain, following up a 1-1 draw with Spartak in their opening group game.
But Maribor - 14 games unbeaten domestically - will look to remain more compact and show more threat on the counter-attack at home to Liverpool, knowing that the away team's defence is capable of gifting them goalscoring opportunities.
Yet anything but victory would surely cause huge concern for five-time champions Liverpool's hopes of winning their group - and so the Premier League team will be expected to go all out in search of three points in Styria.
The visitors remain without winger Sadio Mané due to a hamstring injury which will sideline him for up to six weeks.
Maribor are without centre-backs Denis Šme and Marko Šuler due to an operation on a troublesome Achilles tendon and a foot injury respectively.
Liverpool's 21-man travelling squad in full:
Goalkeepers: Loris Karius, Simon Mignolet, Danny Ward.
Defenders: Nathaniel Clyne, Trent Alexander-Arnold, Andrew Robertson, Alberto Moreno, Joël Matip, Ragnar Klavan, Dejan Lovren, Joe Gomez.
Midfielders: Jordan Henderson, Emre Can, Philippe Coutinho, Alex Oxlade-Chamberlain, Marko Grujić, James Milner.
Forwards: Roberto Firmino, Daniel Sturridge, Mohamed Salah, Dominic Solanke.
Recent form (all competitions)
NK Maribor: WWLDW
NK Rudar Velenje 1-2 NK Maribor (Mešanović 52', Bohar 82')
Liverpool 0-0 Manchester United
Liverpool and NK Maribor have never met before in UEFA competition, with Maribor the only Slovenian club ever to reach the group stages of the Champions League.
The Reds' only previous competitive meeting with Slovenian opposition was in the UEFA Cup in 2003-04, when they overcame NK Olimpija Ljubljana 4-1 on aggregate in the first round.
Maribor, meanwhile, have only won of eight meetings with English clubs - losing five. Their only win came at home to Wigan Athletic in the Europa League group stages in 2013-14.
They held Chelsea to a 1-1 draw in Slovenia in the 2014-15 group stages of this competition, though lost the away game 6-0.
Maribor have yet to win any of their seven home matches in the Champions League so far (D3 L4).
Darko Milanič's men have gone 14 games unbeaten (12 this season) in the Slovenian top-flight, winning nine and drawing five.
Maribor have not won a Champions League group stage game since beating Celtic away from home in August 2014.
Liverpool have won just two of their last 14 European away games (D7 L5) - their most recent a 2-1 triumph in their play-off first-leg against TSG 1899 Hoffenheim in August.
Liverpool have drawn their last four consecutive Champions League games - the first time they have done so since March 2002.
The Reds are on their longest winless run in the Champions League having not won in seven, losing three, since beating PFC Ludogorets Razgrad at Anfield in September 2014.
Liverpool have not kept a clean sheet in this tournament since November 2009 against Debrecen, conceding in all of their past nine games.