Wolves controlled early on against a Liverpool squad that had three changes from the 3-0 victory over Aston Villa and included 20-year-old Jarell Quansah in his first appearance.
Joel Matip, 32, saw himself skinned by Pedro Neto after a Reds attack broke down, and the ball was cut across for Hwang Hee-chan to shoot in via Alisson.
Following a 6,000-mile flight from the high altitude of Bolivia days earlier, Alexis Mac Allister in particular struggled as the No. 6 for Liverpool in the opening half-hour.
After Neto outran Joe Gomez on the wide side, his skillful cross found Matheus Cunha, but the striker blew it terribly.
Cody Gakpo, who was completely absent at the other end, followed suit and (technically) fired one of the few shots for the visitors, scuffing Andy Robertson’s drilled cross way wide of the goal.
Mo Salah and Dominik Szobsozlai were both upset as the half finished with a flurry of attempts in the Wolves penalty area, but due to players blocking their path.
At the half, Mac Allister was freed of his ailing duties and Luis Diaz was introduced as Gakpo moved into midfield. This was a risky and necessary adjustment made by Jurgen Klopp.
Gakpo and Diogo Jota were the players that were removed, and ten minutes later, as the manager was preparing two more, they had a part in the equalizer: Jota found Salah, whose driven ball was tapped in by Gakpo for 1-1.
Harvey Elliott and Darwin Nunez gave the Reds new life, and it took Jose Sa making a big stop to deny the latter following a well-executed play.
With Wolves acting more passively as they sat in, the opportunity appeared certain as Liverpool’s momentum shifted in their favor.
And when it did, it was scored by the most unlikely of players, with Andy Robertson initiating and capping the move with a one-two off of Salah and a straightforward attempt from the skipper.
Elliott’s deflected goal gave the team a 3-1 victory with time remaining for Salah to complete his hat-trick off assists.