Dominik Szoboszlai’s superb first-half strike set the Reds on their way to victory on Wednesday night, and Jürgen Klopp’s side cut loose after the break.
Curtis Jones scored twice and further goals from Cody Gakpo and substitute Mohamed Salah secured both a commanding win and a last-four tie versus Fulham.
Klopp made six changes to the team that had started the goalless draw against Manchester United on Sunday.
Caoimhin Kelleher began in goal, with Joe Gomez and Jarell Quansah brought into defence. Jones, Gakpo and Harvey Elliott also came in, with Salah and Trent Alexander-Arnold among the Reds’ substitutes.
Kelleher, Gomez, Endo (Alexander-Arnold, 60), Van Dijk (Konate, 60), Szoboszlai (Salah, 60), Nunez, Jones, Gakpo (Diaz, 78), Elliott, Tsimikas (Bradley, 69), Quansah.
Unused subs: Adrian, Clark, Gordon, McConnell.
Liverpool started at a good pace, with Szoboszlai the first player to try his luck inside the first four minutes. The Hungarian’s shot, though, struck Darwin Nunez.
Elliott then arrowed a good effort wide from 20 yards as the Reds looked to press home their early dominance, and the youngster was inches away from the opening goal on 14 minutes, sending his effort wide from the edge of the box after good work from Jones.
Nunez headed Szoboszlai’s cross wide and both Elliott and Szoboszlai had further efforts from distance, with Jones seeing a 25-yarder held by Alphonse Areola.
The Reds’ willingness to shoot from outside the box paid off on 28 minutes as Szoboszlai collected Quansah’s pass and fired an unstoppable strike across Areola and into the bottom corner of the net for the opening goal.
Gakpo almost doubled Liverpool’s advantage on the stroke of half-time, heading just wide after a fine cross from the impressive Elliott.
After the break Nunez forced a save from Areola after some tidy footwork in the penalty area, while Jones dragged a 20-yard shot wide from Wataru Endo’s pass.
A superb intervention from Kostas Tsimikas at the far post stopped Jarrod Bowen from finding Pablo Fornals, and soon after Liverpool extended their lead in style.
Nunez was the provider, sliding a perfect pass through to Jones, who slipped the ball through Areola’s legs from an acute angle for his first goal of the season.
Liverpool made a triple substitution almost immediately, with Salah, Alexander-Arnold and Ibrahima Konate replacing Szoboszlai, Endo and captain Virgil van Dijk.
Elliott was denied a deserved goal by Areola after a lovely reverse pass from Salah, and then Alexander-Arnold fired in a cross-shot that Nunez just failed to turn in at the far post.
Liverpool got their third when Konate’s break from defence saw the ball worked to Gakpo, who struck a sweet strike low past Areola from the edge of the box on 71 minutes.
West Ham did get themselves on the scoresheet, Bowen finding space to curl a fine effort beyond Kelleher from Ben Johnson’s pass 12 minutes from time.
But they were finished off by Salah, who ran onto Alexander-Arnold’s sublime through ball to slot home, and by the brilliant Jones, who waltzed his way past four Hammers defenders to fire home five minutes from the end.