In another game, Tottenham Hotspur forward Son Heung-min scored a goal in each half as the London side extended their unbeaten run in all competitions to 17 games with a 2-0 win over Huddersfield Town at Wembley.
Alex Oxlade-Chamberlain's ability to play anywhere across the midfield has often ended up being to his detriment rather than his benefit.
When Egyptian global Salah gave Liverpool the lead after 40 minutes it was his 32nd goal of the season in all competitions for Liverpool and the seventh game in succession that he had found the net.
And Sadio Mane made it 2-0 in the 55th minute when he coolly finished from close range.
Handsome passing combinations and superb movement led to Roberto Firmino setting up Mane, with the Senegal forward - involved earlier in the sweeping attack - beating Dubravka with a super curling strike.
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Mohamed Salah Continues Hot Streak as Liverpool Cruise Past Newcastle
Defeat for former Liverpool manager Rafa Benitez at least came with the consolation of receiving a warm welcome from supporters of both new and old clubs and, at one stage, the entire ground at Anfield chanted his name in unison.
Yet Newcastle failed to trouble Karius again and were perhaps fortunate not to end the game with 10 men after Jamaal Lascelles pushed Salah over in stoppage time when he was the last man. Roberto Firmino the other member of the Reds' front three, helped with an assist for Mane's goal.
He added: "Look, if he was not a good goalkeeper I would be the biggest idiot in world football if I line him up".
"It is tough but it isn't about me, it's about West Brom and it is tough for the fans and the players". "Not only him; there are a few more players", said Klopp. Working that plan out was never going to be Liverpool's problem because they knew it was coming. For goalkeepers, the timing is important.
But as the manager concluded the subject today, Karius is performing well in the moment and that is enough for the player and the team for now. We will see how that improves.
As has become his standard practice against the Premier League's elite, Benitez sent Newcastle out in an ultra-defensive formation, yet the Magpies might still have gone in at the interval on level terms from their only noteworthy attack of the game.