Liverpool’s “little” advantage over Borussia Dortmund, Jürgen Klopp had claimed, lay in the knowledge his revival of the German club began by bringing favourites to their knees. His old club remain standing but his new one have the semi-finals of the Europa League within their grasp thanks to an accomplished display at Signal Iduna Park.

From Dortmund’s perspective, the reunion with their popular former manager fell flat. Klopp set out to frustrate Thomas Tuchel’s side with supreme organisation, defensive resilience and the strength of Divock Origi leading the Liverpool attack. The visitors delivered on every count and the end result, enhanced by Origi’s potentially precious away goal, was their finest European away performance since the Rafael Benítez era.

Mamadou Sakho and Dejan Lovren were commanding in the face of Dortmund’s much-vaunted but ultimately frustrated attack. The only negatives for Klopp were a potentially serious knee injury suffered by Jordan Henderson, one that threatens to sideline the Liverpool captain from the European Championships, and one defensive lapse that allowed Mats Hummels to equalise shortly after half-time.

Otherwise, despite all the pre-match talk of Dortmund’s developed style and cutting edge, Liverpool left knowing they have little to fear from their quarter-final opponents. Tuchel was indebted to several outstanding saves from Roman Weidenfeller for limiting Liverpool to just the young Belgium international’s first European goal for the club.

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Klopp strolled back out at Signal Iduna Park 35 minutes before kick off, giving a polite little wave to the Yellow Wall and studying his former players intently as they went through their warm-up, before attention turned towards his current charges. There, Daniel Sturridge trained among the substitutes having paid the price for a subdued display against Tottenham Hotspur on Saturday and his manager’s preference for the movement and physicality of Origi. It was a major call to start a raw 20-year-old over the team’s leading striker, vindicated when Origi stunned Dortmund with the opening goal.

The Liverpool manager also made a tactical decision to combat Dortmund’s creativity in central midfield by switching James Milner to the left of a central three. Alongside Emre Can and Henderson, Milner added strength and stability to the visitors’ performance as they absorbed pressure but the talents of Henrikh Mkhitaryan and Julian Weigl could not be suppressed completely. The pair’s influence increased in tandem with the home side’s control in the first half, though it was not reflected on the scoresheet.

Tuchel’s team made an edgy start, with loose passes and careless first touches indicating the distraction of Klopp had got to them and undermining attempts to seize the initiative. Maybe it was a coincidence that the biggest culprits, Lukasz Piszczek and Erik Durm, were the two players in yellow closest to their former manager as they patrolled the flank in front of the technical areas in the first half. Gradually, however, Dortmund’s quality pressed Liverpool back and it required two crucial interceptions from Sakho to prevent the German side taking the lead.

Weigl, the impressive 20-year-old midfielder, released Marcel Schmelzer behind the Liverpool defence with a sweeping pass over the top. The left back controlled and cut the ball back for Mkhitaryan but, with the Armenian’s shot destined for Simon Mignolet’s net, Sakho stretched out one of his telescopic legs and diverted the danger. The French central defender repeated the trick when Pierre-Emerick Aubameyang broke down the left and attempted to find Marco Reus unmarked in front of goal.

The pressure intensified, the game flowed in one direction. Aubameyang’s free-kick was deflected just wide and Mkhitaryan went close before, with Dortmund dominant, Liverpool struck. Alberto Moreno’s cross was headed on by Milner. Origi read the midfielder’s intentions quicker than any home defender and pounced on the ball, held off Piszczek on the edge of the area and steered a low shot back inside Weidenfeller’s right hand post. Klopp fist-pumped the one corner of the stadium that did not fall silent.

Dortmund descended from control to chaos in an instant and only last-ditch defending prevented Nathaniel Clyne and Milner doubling Liverpool’s lead moments later. Origi should have done so with the last kick of the half when played through the home side’s suspect defence by Moreno, but his attempted chip was too close to Weidenfeller. Moreno did not hide his disgust at the missed opportunity and his instinct proved correct moments after the restart.

Liverpool had delivered a disciplined away display, making Dortmund’s equaliser all the more galling for Klopp when his team switched off at a short corner and gave Mkhitaryan freedom to sweep a left-footed cross into their penalty area. The imperious Hummels towered above Adam Lallana to steer a header beyond Mignolet’s grasp. Klopp later took responsibility for the goal, revealing he ordered Lallana to mark that area instead of Origi.

The visitors were stung into a response and Weidenfeller made excellent saves from Philippe Coutinho, Clyne and Coutinho again as Liverpool unnerved the German defence frequently. Dortmund’s vulnerability at the back offers further encouragement for Liverpool at Anfield next week, as does their growing maturity on the European stage.