Jeriel Dorsett, under pressure from Issa Diop, knocked the ball into his own net to give the visitors the lead as half-time approached.
Highly rated Conor Coventry doubled the Hammers' lead before the hour mark, tucking home a fine Ben Johnson pass, before Johnson wrapped up the win with a fine solo finish.
David Moyes handed starts to both Coventry and Armstrong Oko-Flex alongside captain Mark Noble in central midfield, and the former Celtic man step up Pablo Fornals for an attempt on goal inside four minutes.
It was a relatively even half until Jarrod Bowen's corner deflected off Dorsett for the opener.
Said Benrahma, wearing the No22, was among the half-time introductions, and he was involved in the build-up for the second goal as Nathan Holland played in Johnson to tee up Coventry for a tap in.
Holland almost get in on the act himself, after fine work from Manuel Lanzini, another half-time substitution, but was tackled while pulling the trigger.
Johnson then jinked past three before slotting home, and Benrahma's late volley flew agonisingly off target.