With the victory, Liverpool moves up to second place in the standings with 16 points, two points behind first-place Manchester City. West Ham drops to seventh with 10 points.
Darwin Nunez, a striker for Liverpool, scored an outstanding goal around the hour mark to help his team cruise to a 3-1 Premier League victory over tenacious West Ham United.
In the seventh minute, Tomas Soucek's downward header forced an incredible save from Alisson, and two minutes later, Michail Antonio headed a Soucek cross wide with the goal at his mercy.
The Egyptian forward was brought down by Nayef Aguerd in the 15th minute for a stonewall penalty, and he stepped up to score the next spot kick to give Liverpool the lead, leaving the Hammers to repent their early errors.
This gave the home team a boost, but West Ham still managed to draw even before halftime when Jarrod Bowen dove at Virgil van Dijk's feet and scored with a beautiful low header for his fourth goal of the year.
The score was uncannily reminiscent of the James Ward-Prowse goal against Manchester City a week prior, but once more it wasn't enough to give it a victory.
Nunez missed a few good scoring opportunities before, largely to the pleasure of the Anfield crowd, latching onto a wonderful lofted pass from Alexis Mac Allister.
The Hammers lost their momentum following that goal, and four minutes after coming off the bench, substitute Diogo Jota was able to score a third goal off Virgil van Dijk's deflection in the 85th minute.
With the victory, Liverpool moves up to second place in the standings with 16 points, two points behind first-place Manchester City. West Ham drops to seventh with 10 points.
Ansu Fati and Kaoru Mitoma were brought on by Brighton coach Roberto De Zerbi at halftime after the Seagulls had fallen behind to Dominic Solanke's opportunistic goal. Brighton went on to defeat Bournemouth 3-1 in the Premier League on Sunday. De Zerbi had made nine changes to his starting lineup from Thursday's Europe League loss to AEK Athens.
Just 15 seconds into the second half, the pair combined for an amazing goal, with Mitoma adding the final touch.
The victory was subsequently sealed by Japanese winger Mitoma with a late header, ending the Cherries' winless start to the league season.
With five victories in six games, high-flying Brighton is third, three points behind leader Manchester City.