Just two weeks on from thrashing the same opponents 7-0 in Slovenia, the Reds found things more difficult on home soil but second-half strikes from Mohamed Salah, Emre Can and Daniel Sturridge ensured that they came away with all three points.
The victory, coupled with Sevilla's 2-1 win over Spartak Moscow in the group's other game, leaves Liverpool now three points clear of third place, while Maribor's slim hopes of breaking into the top two themselves remain alive despite their defeat on Merseyside.
Liverpool, who were again without injured duo Philippe Coutinho and Dejan Lovren, quickly took control of possession, but the early stages suggested that Maribor would be a lot harder to break down than they were in the home hammering at the hands of the Reds a fortnight ago.
Some important interceptions from Jean Billong helped to keep Liverpool at bay in the opening exchanges, and the home side's frustrations were heightened when they lost Georginio Wijnaldum to injury after just 17 minutes.
Despite their dominance Liverpool were forced to wait until the 25th minute before they had their first clear sight of goal, but Salah could not react in time to turn Trent Alexander-Arnold's cross goalwards.
The closest the hosts came to breaking the deadlock in opening 45 minutes came after half an hour when Alex Oxlade-Chamberlain's cross was met by Roberto Firmino and then looped up off Billong, forcing 39-year-old goalkeeper Jasmin Handanovic into an acrobatic save to claw it onto the crossbar.
Liverpool's pressure continued to grow as they pushed for the opening goal, but Can, Salah and Firmino all failed to make the most of half-chances after finding space inside the area.
Firmino had another opportunity to find the breakthrough with nine minutes remaining until half time when he was left unmarked in the penalty area, but he couldn't get enough on his header to steer it goalwards.
Having scored four goals from 12 shots in the first half of the reverse fixture a fortnight ago, Liverpool went into the break goalless from 13 shots at Anfield, although this time there were far fewer clear chances created by Jurgen Klopp's side.
It took only four second-half minutes for them to rectify that, though, as Salah broke the deadlock with his 10th goal of the season when he darted in front of his man to flick Alexander-Arnold's cross past Handanovic.
There was nothing the veteran shot-stopper could do about that one, but he did keep Maribor in the game shortly afterwards with a couple of important saves in quick succession.
The first came from the penalty spot after Firmino was brought to ground having skilfully beaten his marker, with James Milner seeing his subsequent spot kick brilliantly tipped onto the post by Handanovic.
The Slovenian, who will turn 40 in January, made another fine stop to deny Firmino from close range just two minutes later before Salah became the next to squander a clear chance when he nodded an effort over the crossbar when he really should have scored.
Having dropped points as a result of their wastefulness in their opening two Champions League group games, Liverpool were given a reminder that a one-goal lead may not be enough when first Jasmin Mesanovic and then Billong provided rare Maribor threats in quick succession.
Martin Milec then fired an effort over the crossbar as Maribor began to ask more questions of the Liverpool defence, but the hosts effectively killed the match off shortly after the hour mark when Can played a slick one-two with Milner before tucking a confident finish into the bottom corner.
Loris Karius was only called into his first save of the evening with a little over 20 minutes remaining, but Liverpool's Champions League keeper needed to be alert to turn Milec's well-struck low drive away from goal.
The hosts were quickly back on the front foot, though, and Salah and Alexander-Arnold both threatened to increase their lead in the final 20 minutes before Sturridge came off the bench to add the third.
A short corner allowed Alberto Moreno to whip the ball into the box, and with the defence only able to flick it on to an unmarked Sturridge at the back post, the striker was left with a simple finish to score his first Champions League goal for the club.
The result means that Liverpool only need to beat Spartak Moscow at Anfield on matchday six to guarantee their place in the knockout stages for the first time since 2008-09, although their next match sees them face an away trip to Seville.
The Reds have now won back-to-back Champions League games for the first time since that 2008-09 campaign, in addition to consecutive home wins in any competition for the first time since August.