Liverpool did not repeat their rout of Maribor but demonstrated improvement nonetheless. Anfield has been frequently frustrated by opponents like the Slovenian champions – devoid of ambition – but without Philippe Coutinho, Sadio Mané and Adam Lallana, Jürgen Klopp’s team found the answer. Victory was a reward for patience, self-belief and experience.

“We are better equipped for these games because we are more used to them,” said Liverpool’s fortune-teller of a manager after Mohamed Salah, Emre Can and the substitute Daniel Sturridge sealed the win. Klopp had predicted Saturday’s defeat of Huddersfield Town would be perfect preparation for the Champions League tie and so it proved with unerring accuracy. A goalless first half preceded a comfortable win. There was even a missed penalty, Liverpool’s fourth in succession at Anfield, to echo the game against David Wagner’s side.

Maribor restored some pride following their 7-0 humiliation while Liverpool strengthened their claims on the knock-out phase of the Champions League. Qualification will be assured should Klopp’s team become the first to win in Sevilla in over a year later this month. The Liverpool manager said: “Patience is always very important in football. The first half was not the most exciting football, the box was full of people in Maribor shirts, and we had a few problems with the final pass. But like the last game, at half-time the boys knew they had to stay patient and speed up the counter-pressing.”

Liverpool suffered an early setback when Georginio Wijnaldum twisted his right ankle while closing down a Maribor midfielder. Klopp’s attempt to rest Jordan Henderson lasted all of 17 minutes as the captain was summoned to replace the pained Holland international. “Wijnaldum’s ankle was already swollen at half-time,” Klopp said. “Not a good sign.”

There was an immediate blow for any Liverpool supporter expecting another 7-0. Darko Milanic, the Maribor coach, set up his team with nine outfield players behind the ball in a clear damage-limitation ploy. There was to be no repeat of the disorganised display that exposed Maribor’s defence to the Liverpool press a fortnight ago. It made for another episode of attack-versus-defence at Anfield.

Liverpool again dominated the Slovenian champions but lacked the clinical touch that delivered the biggest away win in the club’s rich European history when they last met. With space restricted, the home side’s most productive outlet was Trent Alexander-Arnold and his crosses from the right wing. Salah, Can and Roberto Firmino were unable to capitalise on inviting deliveries from the young full-back before the interval. Alexander-Arnold’s cross for Firmino almost produced the breakthrough with the ball deflecting off defender Jean-Claude Billong towards his own goal. Jasmin Handanovic produced a superb save to claw the ball on to his crossbar.

Maribor departed to a roar of approval from their fans with the game goalless at half-time. Their defiance was short-lived. Liverpool’s movement and passing was much sharper from the start of the second half, another similarity with Saturday, and they were quickly rewarded. A right wing cross from Alexander-Arnold was unsurprisingly key. The 19-year-old picked out Salah’s run across the penalty area with a low, measured delivery. Salah steered the ball beyond Handanovic with a deft finish for the 10th goal of his short Liverpool career. And to think he could have doubled that tally with a touch more composure.

A second should have arrived from the penalty spot when Firmino embarrassed Aleksander Rajcevic with an exquisite flick, prompting the Maribor defender to drag him to the ground. James Milner was handed penalty duties after Salah’s miss against Huddersfield but suffered the same fate as the Egypt international. Handanovic produced a superb save to tip the midfielder’s precise effort on to a post and out.

Maribor’s goalkeeper also denied Firmino at close range and was a bystander when Salah headed wastefully over from Alberto Moreno’s perfect cross, though a Liverpool victory was not in doubt after the opener.

Can secured the three points with a polished second. Cutting across midfield, the Germany international played a slick one-two with Milner before stroking a first-time finish into the bottom corner from the edge of the penalty area. It fell to Sturridge to complete the scoring when he collected Moreno’s cross while Maribor slept at a short corner and fired beneath Handanovic from close range.

“It was not the best we’ve ever played but we knew the maximum points we could have tonight was eight,” Klopp said. “So three more points and a clean sheet – perfect.”