The front three of Roberto Firmino, Philippe Coutinho and Mohamed Salah were all on the scoresheet inside the opening 20 minutes, before Salah and Firmino doubled their personal tallies either side of the interval.
Alex Oxlade-Chamberlain then opened his Liverpool account late on before Trent Alexander-Arnold capped off the rout in the final minute of normal time, sending Liverpool to the top of Group E in emphatic fashion.
Find out how all of the action unfolded on a memorable evening for the Reds courtesy of Sports Mole's minute-by-minute coverage below.
Both of these sides are still searching for their first win of the campaign proper having needed qualifying to reach the group stages, but it is Liverpool who will head into tonight's match as favourites despite Maribor boasting the home advantage.
It promises to be a pivotal night for the Reds' hopes of reaching the last 16, so let's waste no time in getting to the team news...
Well, we'll get onto Liverpool in a moment but first let's have a brief look at the Maribor starting XI as manager Darko Milanic makes just two changes from the side that was beaten 3-0 by Sevilla in their last Champions League outings. Those switches see Suler and Kramaric come into the lineup, while Billong and Pihler drop to the bench.
Mesanovic may feel slightly hard done by to miss out having scored at the weekend, but Brazilian striker Marcos Tavares was always expected to come back into the side and sure enough he does tonight. Ahmedi, Suler, Kramaric and Kabha are the other four players to return having been left out at the weekend.
Philippe Coutinho, Mohamed Salah and Roberto Firmino all start against for Liverpool having also played at the weekend against Manchester United, with the injured Sadio Mane the only major absentee from Liverpool's forward players tonight. Dominic Solanke and Daniel Sturridge provide the firepower off the bench.
Milner, of course, spent the majority of last season playing at left-back, but Alberto Moreno's rejuvenated form in that position has seen him revert to midfield - although that has also severely limited his game time so far. Milner is such a reliable player, though, and he will be desperate to take this chance tonight.
The deadline-day signing has not started in the Premier League or Champions League for Liverpool yet, and his chances will surely only become more limited once the likes of Adam Lallana and Sadio Mane return from injury. The former Arsenal man is having to be very patient so far.
Gomez was available for this match having served a one-game ban against Spartak Moscow in Liverpool's last Champions League game, but having also featured against Manchester United Klopp has decided to rotate his full-back again tonight. Clyne remains sidelined which is why the question arises in the first place, but Alexander-Arnold has shown a lot of promise so far and will have another chance to shine tonight.
Klopp has settled on Karius as his Champions League keeper so far this season, with the 24-year-old starting all three group games so far, but Karius has also expressed his desire to impress enough to become the first choice in the Premier League too. However, he has conceded three goals from the four shots on target he has faced in the Champions League this term, so he has work to do.
Matip and Lovren both start at the heart of the defence once again - as they did against United and Moscow - while Moreno continues at left-back, where he has re-established himself as first choice at Anfield.
For Maribor, anything other than defeat against the five-time champions of Europe would have to go down as a very good result. Their European pedigree cannot come anything close to Liverpool's with this just their third appearance in the group stages of the Champions League.
From seven previous home games in the competition proper, Maribor have picked up just three points from a possible 21, although that does include a draw at home to Chelsea in their last group-stage campaign before this season.
When it comes to the higher level of competition which takes place in the group stages, though, the Slovenian champions fall short. Indeed, last season they didn't even make it into Europe proper, bowing out in the playoffs of the Europa League.
Maribor overcame opposition from Bosnia, Iceland and Israel to book their place in the competition proper, but their wait for a Champions League group-stage win now stretches to 13 matches following a draw with Spartak Moscow and heavy defeat to Sevilla so far.
In all of that time the Slovenian champions have never scored more than a single goal in a game either, although including qualifiers and the Europa League they do at least come into this match having lost just three of their last 14 European outings.
Darko Milanic's side find themselves two points adrift of leaders Olimpija Ljubljana after 12 games of the campaign, and with only top spot having the chance to qualify for the Champions League next season they will know that second place is not good enough by their recent standards.
Aside from losses to Hapoel Be'er Sheva in the playoffs and Sevilla in their most recent European outing, Maribor have won 13 and drawn six matches this season, while the loss to Sevilla is their only defeat in their last 11 matches. In the league alone they are four points better off than at the same stage last season and, including the tail end of the 2016-17 campaign, are unbeaten in 14.
There has not been a great deal wrong with Liverpool's all-round performances in recent weeks, but they have failed to make the most of their possession on numerous occasions to leave them with just one win from their last eight matches across all competitions - a run which includes three consecutive draws heading into tonight's match.
The result leaves the Reds eighth in the Premier League table and, while just two points separate them from the top four, they are now nine points adrift of in-form Manchester City and their title hopes are already fading badly with just eight games of the new Premier League season having gone.
Liverpool should have six points on the board already considering how much they have dominated both of those games, but despite having 29 more shots than their opponents in those outings - 17 against Sevilla and 12 against Spartak - they have failed to win either.
Having said that, the aforementioned stat of Liverpool conceding three goals from just four shots on target in the Champions League proper so far this season is pretty damning, and the lack of chances put away would not have been highlighted so much if Liverpool didn't have such a penchant for shooting themselves in the foot at the other end of the field.
That triumph over Debrecen was also Liverpool's most recent away win in the Champions League proper, and their only triumph in eight attempts since beating Real Madrid of all teams at the Bernabeu in February 2009.
That streak includes three defeats and four consecutive draws heading into this match, and Liverpool will know that a failure to end that run this evening - coupled with a victory for Sevilla in Moscow - would leave them with a mountain to climb in order to claim top spot in Group E and potentially an easier draw should they make it into the last 16.
Indeed, Liverpool are in the group stages of the Champions League for only the second time in the last eight seasons this term, and have not reached the knockout stages since 2008-09, so perhaps we should not be so surprised that they have made a relatively slow start.
Liverpool have not been in great form heading into this one, but simply put they have the better players and should have enough about them to come away with a win tonight. Maribor may try to stifle the Reds as a few teams have successfully managed to do in recent weeks, but we're backing an away win.
SPORTS MOLE SAYS: Maribor 0-2 Liverpool
The first of those came in the opening round of the 2003-04 UEFA Cup, when Liverpool could only manage a 1-1 draw in Slovenia against Olimpija Ljubljana. The Reds did pick up a 3-0 victory in the return leg at Anfield to progress, but they are looking for their first win on Slovenian soil tonight.
Just one of those has come in the Champions League, and that turned out to be a successful night for Maribor as they earned a 1-1 draw against Chelsea having lost the reverse leg 6-0 at Stamford Bridge.
The solitary triumph was a 2-1 win over Wigan Athletic in the 2013-14 Europa League group stages, and they have never kept a clean sheet against an English club in this eight previous meetings.
MARIBOR STARTING XI: Handanovic; Suler, Bohar, Viler, Milec; Rajcevic, Ahmedi, Kabha, Vrhovec; Kramaric, Tavares
LIVERPOOL STARTING XI: Karius; Alexander-Arnold, Matip, Lovren, Moreno; Milner, Wijnaldum, Can; Salah, Coutinho, Firmino
Salah beats Suler to the ball down the right flank and that sees him flying clean through on goal down the channel. Firmino is in support through the middle and it is a simple enough pass for Salah to pick the Brazilian out, who is left with an even easier finish.
It could be a long night for Maribor.
Elsewhere, Feyenoord lead Shakhtar Donetsk and RB Leipzig are ahead against Porto.
It is a really nice move from the visitors as Firmino gives it out to Milner, who pulls a clever cross back into the box. Coutinho meets it with a scuffed finish, but it is crucially on target and nestles into the bottom corner.
His clever pass inside the full-back releases Salah in the area and he has time to take a touch before stroking his finish past the keeper from close range. This could be a cricket score if things carry on like this.
As things stand, then, Liverpool will be heading to the top of Group E tonight.
Liverpool scored 3-0 in 19th minute. When they claimed the CL's biggest win - 8-0 Besiktas (2007) - they scored their 1st goal in 19th min.— Gracenote Live (@GracenoteLive) October 17, 2017
Moreno is the creator, reaching the byline down the left flank before pulling a low ball across the face of goal. Both Firmino and Salah are left waiting for the simplest of finishes, and it isn't quite clear who gets the final touch. Salah is being given the credit at the moment, though!
This one is over as a contest and has been since the 20th minute, with Liverpool racing into a 3-0 lead before adding a fourth late in the half. It has been an irresistible display from Jurgen Klopp's side, and they are by no means finished yet.
Salah pounced on an underhit pass down the right flank to beat Suler to the ball and lay it across for Firmino, who tucked it into an unguarded net from close range to get Liverpool off to a perfect start.
A third arrived after just 20 minutes too, as Firmino and Salah reversed their roles from the first goal with the Brazilian playing in the speedy winger, who calmly stroked the ball past the keeper from inside the area.
Moreno's low ball across the face of goal left Firmino and Salah both queuing up to put it in, and the latter looked like he just about beat his teammate to the punch.
Salah is still being credited with the second, but that may well be a hat-trick goal for Firmino as he produces a deft finish to glance a backward header into the far corner from Coutinho's free kick.
Elsewhere, Shakhtar Donetsk now lead Feyenoord, Besiktas are 2-1 up against Monaco, RB Leipzig lead Porto 3-2 and Real Madrid have levelled things up against Tottenham.
Elsewhere Borussia Dortmund had fallen behind against APOEL, but they have since levelled things up in Tottenham's group.
It is another error from the hosts as Suler gives the ball away, and Sturridge picks it up before threaded a nice weighted pass into the path of Oxlade-Chamberlain. That sends the midfield through on goal, and he makes no mistake with his finish.
The Slovenian hosts were poor and did not help themselves at all tonight, but take nothing away from a rampant Liverpool performance as they set a new British record for the biggest ever away win in the Champions League. Roberto Firmino (2), Philippe Coutinho, Mohamed Salah (2), Alex Oxlade-Chamberlain and Trent Alexander-Arnold were all on the scoresheet for the visitors on a record-breaking and memorable night in Maribor.
Thank you very much for joining Sports Mole for tonight's Champions League clash as a record-breaking Liverpool display sees them fire seven past Maribor on their way to the top of Group E. I will leave you with our match report, and be sure to stick around for reaction too.
From me, though, it is goodbye for now!