Substitute Mohamed Salah scored the fastest hat-trick in Champions League history, with the Egypt winger's first and third goals only six minutes and 12 seconds apart from each other as the Reds made it seven heaven in a one-sided second half.
Scott Arfield had earlier sent Ibrox into delirium by latching onto Ryan Jack's pass during a slick counter-attack from the hosts, with the former Burnley midfielder tidily slotting the ball into the bottom corner and beyond the reach of Alisson Becker in the 17th minute.
However, Roberto Firmino continued his excellent goalscoring form to bring the visitors level from Kostas Tsimikas's corner seven minutes later, with the Brazil forward outmuscling James Tavernier at the near post to guide a well-timed header into the back of the net.
Rangers looked marginally threatening in a fairly quiet first half, with Fashion Sakala beating Tsimikas all ends up down the right flank before cutting the ball back to find Arfield, who this time saw his effort blocked by Ibrahima Konate.
The hosts lost key defender Connor Goldson to a potentially serious thigh injury moments before the break, with the former Brighton & Hove Albion defender's absence seemingly keenly felt as Jurgen Klopp's side ran riot to secure a comfortable victory and move only one point away from progressing to the knockout stages in the process.
Firmino rifled the visitors ahead from Joe Gomez's excellent cross, before the Brazilian unselfishly squared the ball for Darwin Nunez, who accurately curled the ball around the reach of Allan McGregor and into the far corner to give Liverpool breathing space.
It was the Salah show from there, with Liverpool's key man finally finding some form ahead of Sunday's huge clash against Manchester City in the Premier League after being introduced in the 68th minute.
The 30-year-old showed dazzling skill and composure for all three of his trademark goals, which were each created by fellow substitute Diogo Jota, before Harvey Elliott bagged his first ever European goal late in the match after a lengthy VAR check kept the 19-year-old waiting.