The Reds, who had drawn their opening Champions League games, were under pressure to beat the minnows but once they raced into a 3-0 lead inside twenty minutes, the result was never in doubt.
Liverpool’s pace and swift interchanges left Maribor’s defenders looking like they were flat-footed as the likes of Roberto Firmino, Philippe Coutinho and Mohamed Salah al sc
Salah would then add his second and Liverpool’s fourth of the night five minutes before the interval to give the visitors a commanding lead.
Firmino would then double his tally for the night with a glancing header from a Coutinho free-kick in the 54th minute as the rampant Reds continued to score with ease past their hapless opponents.
With one eye on a Premier League clash with Tottenham Hotspur on Sunday, Jurgen Klopp took off Salah for Alex Oxlade-Chamberlain before the hour-mark and the substitute registered his first ever goal for the club four minutes from time.
Daniel Sturridge, another substitute, set up the Chamberlain with a perfectly weighted through-ball and the midfielder responded with a cool finish past Jasmin Handanovic.
Maribor’s misery would be compounded when Liverpool fullback Trent Alexander-Arnold scored the away side’s seventh in the 91st minute.
There was a huge upset in the other UEFA Champions League Group E game on the night, as Russian side Spartak Moscow spanked Sevilla 5-1 Otkrite Arena to be level on points with Liverpool.
Klopp’s side, however, are topping the group by virtue of their superior goal difference. The Reds have five points from three matches, as do Spartak while Sevilla third with four points.