Jarrod Bowen had initially cancelled out a Mohamed Salah penalty in the opening 45, but second-half strikes from Darwin Nunez and Diogo Jota sunk the Hammers, as Jurgen Klopp's men prolonged their unbeaten start to the campaign in style.
Captain Virgil van Dijk slotted straight back into the Reds backline following his domestic suspension, while Bowen recovered from illness in time to start for West Ham, demoting Mohammed Kudus to the bench despite his starring role against Backa Topola in the Europa League.
West Ham's plan to hit Liverpool on the counter initially worked a treat, as Tomas Soucek forced Alisson Becker into a terrific save from a downward header in the sixth minute, moments before Michail Antonio squandered a gilt-edged chance from the Czech midfielder's cross.
Those wasted opportunities would come back to bite West Ham, as Nayef Aguerd felled Salah in the box following a quick Liverpool break, and the Egyptian sent Alphonse Areola the wrong way with a venomous penalty to put the hosts ahead in the 16th minute.
David Moyes's side were ostensibly focused on entering the break with just the one-goal deficit to make up, but the Irons stunned the Kop with a leveller three minutes before the break, as Vladimir Coufal's delivery found Bowen, who bravely dived at the feet of Van Dijk and directed a header off the post and into the back of the net.
An open start to the second 45 saw both Nunez and Bowen waste good chances to propel their side into a 2-1 lead, but the former rectified his earlier miss with a fine finish on the hour mark, getting in between the two West Ham centre-backs and delicately toe-poking a volley into the corner from Alexis Mac Allister's ball over the top.
This time, there would be no Irons response, and Jota put the game to bed with 85 minutes on the clock, as Van Dijk knocked the ball down from a corner for the Portuguese to steer the ball home from a couple of yards out.
Owing to Tottenham Hotspur's North London derby draw with Arsenal, Klopp's charges have risen to second in the table behind Manchester City, while West Ham United drop to seventh on account of Aston Villa's win over Chelsea.
Liverpool now gear up for Wednesday's EFL Cup third-round showdown at home to Leicester City, while West Ham visit Lincoln City in the same stage of the competition on September 27.