Josh Pask got the only goal at Liverpool’s Academy, scoring for the Hammers in the third minute at the second attempt.
West Ham had the better chances to double their lead in the first half against a Liverpool side featuring many players from their Under-18s, whose coach Steven Gerrard was in attendance.
Liam Millar, pictured above being tackled by Pask, had a chance to level after the break but headed straight at Nathan Trott in the West Ham goal.
The win lifts West Ham up to sixth on 25 points.
Liverpool: 25 Feb v Stoke (A) PL Cup
West Ham: 2 Mar v Man City (A) PL2