Mohamed Salah and Sadio Mane gave the Merseyside giants a two-goal lead at the break, while the latter added a second shortly after the restart before Daniel Sturridge scored a late fourth with his first touch.
West Ham had their moments in the North-West, but the Hammers were comfortably beaten as they conceded four goals against Liverpool for the fourth game in a row.
Jurgen Klopp and Manuel Pellegrini opted to hand debuts to a combined total of seven summer signings, but it was Liverpool's established front three who impressed during the opening stages as West Ham struggled to cope with their movement.
The home side did not get a shot away until the 19th minute but, when it arrived, it led to a goal as Andrew Robertson delivered a low pass into the penalty area for Salah to tap home from no more than two yards out.
Liverpool's opener acted as the catalyst for a dominant period in the final third, with Trent Alexander-Arnold seeing a free kick superbly kept out by Lukasz Fabianski and Georginio Wijnaldum poking wide from the centre of the penalty area.
West Ham responded with Marko Arnautovic firing wide of the far post and Fabian Balbuena seeing a header comfortably saved by Alisson, but Liverpool were soon back in the ascendancy with Salah somehow failing to find the back of the net from six yards with Fabianski making a point-blank save.
The Hammers appeared to have done enough to head into the break only facing a narrow deficit but in the final seconds of the first half, a cross from Robertson was sent back into the middle by James Milner and Mane could not miss from inside the six-yard box.
West Ham returned for the second half on the front foot and Michail Antonio had the chance to pull a goal back from close range, but the winger sent an overhead kick over the bar after being found three yards out from a corner.
That miss proved to be costly as Liverpool soon extended their lead, although Mane's confident finish from 12 yards should have been ruled out after Roberto Firmino found his teammate in an offside position.
The goal effectively ended the game as a contest and as the match progressed towards the final quarter-of-an-hour, only Wijnaldum came close to adding a fourth with the Dutchman curling over from 20 yards out.
With little action on the pitch, the game was temporarily stopped as a child entered the playing area to hug Salah, and the break in play also led to Xherdan Shaqiri being introduced for his debut.
The match appeared to be petering out but with three minutes remaining, Sturridge was introduced from the bench and the England international scored within seconds of his arrival, tapping the ball home at the back post from a corner.
Antonio got one final effort on goal for West Ham in added-on time, but the visitors were well beaten by a team who barely had to break sweat in order to run out convincing winners.
LIVERPOOL (4-3-3): Alisson; Alexander-Arnold, Gomez, Van Dijk, Robertson; Milner, Wijnaldum, Keita; Mane (Shaqiri 82'), Salah (Sturridge 87'), Firmino (Henderson 69')
WEST HAM UNITED (4-3-3): Fabianski; Fredericks, Ogbonna, Balbuena, Masuaku; Noble, Rice (Snodgrass 46'), Wilshere; Antonio, Anderson (Hernandez 62'), Arnautovic (Yarmolenko 67')