Joel Matip, Alex Oxlade-Chamberlain, Fabinho and Diogo Jota entered as four changes for the Reds, as West Ham brought no alterations from their win over Aston Villa.
The Hammers were off to a dream start inside four minutes after an in-swinging corner-kick from Pablo Fornals coincided with the gloves of Alisson Becker before it cracked the back of the net.
It was then required of the Hammers boss David Moyes within the middle of the first half to make a substitution albeit forced, as Angelo Ogbonna couldn't continue and saw Craig Dawson enter.
Liverpool clawed a way back in the last four minutes of the first half through an exquisite free-kick by Trent Alexander-Arnold that curled over the wall of West Ham before hitting the net.
Moyes's men were close to regaining the lead five minutes inside the second half when a thumping header from Dawson off another well-worked corner by Fornals clattered the bar.
It took the Hammers 17 minutes later to reclaim their cushion as Jarrod Bowen charged on misplaced possession by Liverpool to lay off a pass to Fornals for a bottom low finish.
West Ham added a third near the final ten minutes after Kurt Zouma wiggled unchallenged in the area to head in from an acute angle following a corner by Bowen.
The Reds didn't lose ground eight minutes from time when substitute Divock Origi controlled a loose ball in the area, turned goal-wards to volley into the bottom-corner.
West Ham nearly watched their lead slip away in the dying stages from the head of Sadio Mane following a free-kick, but luckily the forward nodded off target, as it finished 3-2.