Mohamed Salah struck twice, with Roberto Firmino and Sadio Mane also on the scoresheet, to settle Wednesday's largely one-sided Group C contest.
Here are five talking points on the action from Anfield…
Back on track
After a disappointing, below-par evening at Stadio San Paolo three weeks ago, a response was needed.
That it duly arrived while Paris Saint-Germain and Napoli shared a 2-2 draw means Liverpool sit top of Group C at the halfway point of the pool stage.
Next up, a trip to Belgrade.
Salah hits his half-century
Salah’s brace saw him reach 50 goals for Liverpool.
It took the Egyptian only 65 matches to reach the landmark; an astonishing, club-record statistic that goes some way to quantifying the impact he’s made since arriving at Anfield ahead of last season.
His 49th for the club had echoes of his 48th, which arrived at Huddersfield Town at the weekend, as a perfectly-weighted pass from Xherdan Shaqiri preceded a certain right-footed finish.
No.50 came from a penalty early in the second half, before Salah was afforded a richly-deserved standing ovation when being substituted 20 minutes from time.
Captain Virgil
With Jordan Henderson sidelined due to a hamstring issue and James Milner named among the substitutes, Liverpool were captained by Virgil van Dijk for the first time from the start of a match.
The unflappable Dutchman has been imperious all season - and Wednesday night was no exception as he, alongside the outstanding Joe Gomez, marshalled the Reds to a seventh clean sheet of 2018-19.
The Opta data shows that Van Dijk’s 90 minutes included four clearances, 85 passes and five ball regains.
There’s no numerical way of measuring the aura of indomitability the stand-in skipper brings, though.
Stevie, Rushie, Bobby & Mo
Only Steven Gerrard and Ian Rush have now scored more times for Liverpool in the Champions League/European Cup than Firmino and Salah.
The Brazilian’s 20th-minute goal was his 13th in 17 appearances for the Reds in Europe’s elite club competition, while Salah has netted the same number in 18 games.
The duo's goals on Wednesday took them clear of Dirk Kuyt and Terry McDermott and to within one of Rush. Gerrard’s total of 30 remains some way off, though.
It’s also worth noting that since the start of last season, Firmino has been directly involved in 19 Champions League goals (12 goals, seven assists), more than any other player in the competition.
Not bad, lads!
Shimmering Shaqiri
Shaqiri’s ability to combine ingenuity with industry once again made him vital for Liverpool.
As against Huddersfield on Saturday, the Swiss was stationed as part of the Reds’ midfield three.
And, as against Huddersfield on Saturday, he provided a deft assist for Salah.
Shaqiri’s influence was also stamped on Liverpool’s opening goal, as he tracked back to regain possession before sliding the ball into Andy Robertson’s path, from where it made its way into the net via Firmino.
His substitution with 68 minutes gone elicited rapturous and appreciative applause from the Anfield faithful - along with a big, warm hug from Jürgen Klopp.
Match report: Firmino, Salah and Mane strike in Red Star win>>