It took Liverpool 90 minutes to switch off at a set piece against Hoffenheim. Benjamin Hübner met Nadiem Amiri’s free-kick with an unmarked header six yards out and the recurring theme of Jürgen Klopp’s reign made a fleeting reappearance. Not again? Not this time. Hübner headed over and Liverpool found themselves within touching distance of the Champions League group stage – a vast reward for fine margins.

Klopp left his homeland with a precious, timely play-off victory built on the confidence of youth and the value of experience.

Trent Alexander-Arnold, the homegrown right-back who was born a stone’s throw from Melwood, swept Liverpool ahead with a stunning free-kick. The 18-year-old’s first goal for the club arrived on his Champions League debut and, although he was caught out for Hoffenheim’s late consolation, he chose a perfect way to announce himself to a wider audience.

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As for experience, Simon Mignolet saved a first-half penalty having studied Andrej Kramaric’s dubious technique with the goalkeeping coach, John Achterberg. James Milner appeared to have secured the game and the tie with a cross that deflected in off the former West Ham United defender Havard Nordtveit only for Mark Uth to set up a tense finale with a fine finish. It is all to play for but advantage Liverpool.

In truth a two-goal cushion would have flattered Klopp’s team. Their defending, particularly that of Alberto Moreno, once again offered encouragement to their opponents and struck fear into their supporters. Hoffenheim also played with a confidence and adventure befitting their 30-year-old coach Julian Nagelsmann – Milner’s junior – but quality often eluded them in Mignolet’s penalty area, much to Liverpool’s relief.

“We played a good match here and I promise you we will play a good match at Anfield,” said Nagelsmann, who took umbrage at Klopp’s claim that Liverpool had allowed Hoffenheim the ball in unthreatening areas.

“I would have been confident of coming back from 2-0,” he added. “We had great possession in these so-called unimportant areas.”

Hoffenheim controlled the early exchanges and were awarded a soft penalty when the former Arsenal forward Serge Gnabry nutmegged Dejan Lovren having cut in from the right – Moreno’s flank – and went down under a slight touch. Klopp raged at the officials but would have saved his energy with the benefit of hindsight. Kramaric took a short run-up to the spot-kick and placed it weakly down the centre of Mignolet’s goal. The visitors’ keeper barely had to extend himself to make an invaluable save. Liverpool had a reprieve.

Within seconds the Hoffenheim captain, Kevin Vogt, overcommitted himself on the half-way line and invited Mohamed Salah to play a swift one-two with Roberto Firmino. Liverpool’s record signing raced clear from the half-way line but, with only the goalkeeper, Oliver Baumann, to beat and under pressure from the recovering Vogt, he shot wide from the edge of the penalty area.

Pavel Kaderabek sliced over from one of several inviting crosses from the left foot of Kerem Demirbay. Lukas Rupp had a shot blocked and Mignolet saved crucially again when Gnabry escaped behind the Liverpool defence and volleyed from close range. Sandro Wagner put the rebound wide. It was another escape.

By that point Liverpool had a precious lead and away goal. The Hoffenheim central defender Ermin Bicakcic was booked for dragging down the outstanding Sadio Mané 25 yards out. Emre Can and Moreno lined up their options at the free-kick only for Alexander-Arnold to emerge through the pack and sweep a superb finish over the wall and into Baumann’s bottom left-hand corner. The Hoffenheim keeper was rooted to the spot, stunned, along with everyone else.

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Mané was Liverpool’s most potent forward throughout. He glided past Bicakcic twice at the start of the second half to set up an excellent chance for Firmino, who was given a rousing reception on his return to Hoffenheim, but the Brazilian was unable to beat Baumann at close range. Moments later Mané beat Bicakcic again and forced the home keeper into a low save. The Hoffenheim defender was then substituted.

In fairness to Liverpool’s defenders –but not Moreno, who routinely failed to track his runner – they improved significantly after the break. Not even a series of well-taken Hoffenheim corners disrupted Liverpool’s solidity and victory was sealed on account of quick-thinking and Hoffenheim inexperience. Amiri raged at the referee over the award of a free-kick, turning his back on Georginio Wijnaldum in the process. Wijnaldum played the free-kick unhindered to Firmino, who pierced the Hoffenheim defence with a superb ball out to Milner on the left. The Liverpool substitute crossed with his right foot and a slight deflection gave Baumann no chance as the ball sailed inside his far post.

Milner’s importance exceeded the goal because he brought much-needed composure to the Liverpool performance. It was required when Uth, played onside by an appealing Alexander-Arnold and a sleeping Lovren, controlled a long ball from the right on his chest and finally ended Mignolet’s resistance with an excellent low drive.

“I would have taken any win before the game,” admitted Klopp. “Even 8-7.” That might have been possible given the number of chances for both sides, something for the Liverpool manager to consider before next Wednesday’s second leg. It is not over but Liverpool are close.