Back in the UEL for the first time since losing to Sevilla in the 2016 final, Liverpool travelled to Austria full of confidence after a superb start to the domestic season.
An opening clash against in-form LASK promised to be a stern test, however, and it was the hosts who took a shock lead in the 14th minute when Florian Flecker fired a stunning long-range strike into the far corner.
Having fallen behind for the fourth time in their last five matches, Liverpool went in pursuit of an immediate response, but clear-cut chances came at a premium as LASK held firm during a closely-fought opening half-hour.
The visitors continued to probe for an equaliser with HT approaching, however, Tobias Lawal denied Núñez from point-blank range as the Austrian side went into the interval with a slender advantage.
Despite Liverpool’s uninspiring first-half performance, Klopp resisted the temptation to ring the changes at the break, and the visitors were gifted a route back into the contest within 10 minutes of the restart when Philipp Ziereis fouled Díaz in the box.
That allowed Núñez to step up to the spot, and the Uruguayan fired home into the top-right corner to level the scores.
Armed with the momentum, the Reds struck again just seven minutes later through Díaz, who finished brilliantly from Ryan Gravenberch’s driven delivery.
Clearly taken aback by the visitors’ quick-fire double, LASK looked to regain some semblance of composure heading into the final 20 minutes as they chased an unlikely late equaliser.
However, it was Liverpool who added gloss to the scoreline through substitute Mohamed Salah as the Reds secured three hard-earned points, continuing their good form ahead of a home clash against West Ham United at the weekend.
As for LASK, the Austrian side will be desperate to bounce back as soon as possible after suffering just their second defeat in 17 European matches.
Flashscore Man of the Match: Luis Díaz (Liverpool)
See a summary and player ratings from the match at Flashscore!