After drawing their first two European fixtures and spluttering in the Premier League, Liverpool arrived in Slovenia with critics questioning Klopp’s signings and tactics.
But, for once, Klopp’s team showed a ruthless touch in the opposition penalty area to demolish woeful Maribor.
Firmino opened the scoring and Philippe Coutinho increased Liverpool’s lead before Salah’s brace put the Reds four up by half-time at Stadion Ljudski Vrt.
Firmino netted again after the break, with Alex Oxlade-Chamberlain and Trent Alexander-Arnold also on the scoresheet as Liverpool’s goal blitz moved them into first place in Group E with three matches left.
After only one victory in their last eight games in all competitions, this was a welcome tonic for Klopp and company as they ended a three-match winless run.
Now Klopp must hope the dominant display marks a much-needed change in his side’s fortunes.
“Our attitude was really outstanding. We scored wonderful goals and played wonderful football,” Klopp said after Liverpool’s biggest ever European away win.
“I know at the end it looked like Maribor were not good but it was not easy against us today. It was a very mature performance.”
Saturday’s goalless draw against Manchester United had continued Liverpool’s frustrating recent trend of failing to kill off their opponents despite controlling possession.
Liverpool’s profligacy sparked criticism of Klopp’s failure to buy a top-class striker and, irritated by questions about his trophyless two-year reign, he sarcastically labelled himself a “charismatic, funny loser” earlier this week.
Aware the heat was being turned up, Klopp will be relieved Liverpool looked more potent, although it helped that Maribor were totally out of their depth.
Klopp’s side quickly punished Maribor’s naive defending to take a fourth minute lead.
Salah was left in acres of space down the right edge of the Maribor penalty area and the Egypt winger’s low cross into the six yard box teed up Firmino to tap-in his fifth goal of the season.
– Running riot –
Liverpool were running riot and Coutinho doubled their advantage in the 13th minute.
Salah sent James Milner away down the right flank and he pulled a cross back to the edge of the Maribor area, where Coutinho arrived to slot home his fifth goal of the season.
Firmino went close with a flicked shot at the end of a flowing move, but for once applying the finishing touch wasn’t a problem for Klopp’s men.
Salah made it three with his seventh goal of the season in the 19th minute.
Firmino was the creator, riding two tackles and slipping a deft pass to Salah, who guided a cool finish past Maribor goalkeeper Jasmin Handanovic.
Maribor were in complete disarray and Salah notched Liverpool’s fourth from virtually on the goalline after Alberto Moreno’s cross unhinged the hapless hosts in the 39th minute.
It was only the seventh time an English club had scored four first half goals in the Champions League.
Liverpool weren’t finished yet and the Brazil connection combined for their fifth when Firmino rose to head in Coutinho’s 54th minute free-kick.
Capping a night when everything when right for Klopp, Oxlade-Chamberlain, on as a substitute, grabbed his first Liverpool goal since his August move from Arsenal.
Daniel Sturridge’s pass sent Oxlade-Chamberlain clear in the 86th minute and he calmly stroked his shot past Handanovic.
Klopp was all smiles on the touchline and there was still time for teenage defender Alexander-Arnold to net in stoppage-time with a deflected long-range effort.
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