Shaun Donnellan opened the scoring ten minutes in and that lead was doubled a few minutes into the second half when Tunji Akinola turned into his own net.
Tom James all but sealed the victory for the green and whites as he whipped in one of his signature free-kicks 25 minutes from time.
Enes Mahmutovic got involved in the scoring eight minutes from time to ensure that the young Hammers travelled back empty-handed.
Darren Way made the maximum allowance of six changes to the side that somehow fell to a 2-1 defeat at Morecambe at the weekend.
Academy product Daniel Ojo made his professional debut on the left side of defence with Stuart Nelson captaining the side in his first start of the season.
Omari Patrick, Alefe Santos, Alex Pattison and Mahmutovic also came into the starting XI with Alex Fisher remaining out of the squad as he recovers from a virus picked up last week.
With no fresh injuries from the weekend Town remained without Gary Warren, Jordan Green, Omar Sowunmi, Diallang Jaiyesimi, Korrey Henry and James Bailey through injury.
In a cold drizzly evening affair in Somerset it was who Town created the first opening of the game.
A corner from Santos was met by Donnellan but Nathan Trott tipped over smartly to deny the Irishman his first goal in green and white.
There was nothing Trott could do barely seconds later to deny Donnellan however as he met Santos’ corner from the right and converted from a few yards out to give the Glovers the lead ten minutes in and net his first goal for the club.
Despite the hosts being comfortable in possession they were reminded of the danger West Ham posed.
The visitors had their first sight of goal through Jahmal Hector-Ingram, the winger’s shot was deflected and Nelson reacted well to get down and prevent the equaliser.
As the weather began to dry up slightly, seemingly so did the chances just before Jake Gray almost struck a fantastic volley in for Town’s second.
Bringing the ball under control on the right the ball set up perfectly for the volley which was well executed by Gray forcing a good stop from Trott.
Good link up play from Gray and Patrick led to a shot from the Bradford loanee which was held by the United stopper at the near post.
As the rain faded away at the start of the second half so to did West Ham’s hopes of getting back into the game.
Patrick played in Olufela Olomola down the left hand side, the forward beat his man and delivered a ball into the six-yard area which was turned into his own net by Akinola with Arquin lurking behind.
The two goal deficit in no way deterred the West Ham youngsters as they looked to reply instantly, a strike from Dan Kemp was destined for the top corner but Nelson tipped over to leave his goal unscathed.
With half an hour to go Gabriel Rogers and Francois Zoko entered the fray, with the academy product making his fourth appearance for Town.
Showing great promise in his first game for Yeovil, Ojo turned his man and drew a foul on the left hand side of the area 25 yards from goal which set up the third goal.
Becoming a set-piece specialist Tom James lined up the free-kick and the ball dipped over Trott who stood no chance as the Welshman netted his third set-play of the season.
Despite a three goal advantage Town were dealt a blow when Olomola was forced off with an injury with just over 15 minutes to play, however, that didn’t stop the Glovers adding to their already healthy lead.
A free kick was launched into the box by Santos and Mahmutovic was on hand to turn in from a few yards out to net his first goal since joining on loan from Middlesbrough and cap off a succesful home win for Way’s side.
Yeovil Town: Nelson; James, Donnellan, Mahmutovic, Ojo; Gray, Pattison (Rogers 60’), Santos, Patrick; Olomola (McDonald 73’), Arquin (Zoko 60’)
Subs not used: Baxter, Dickinson, Mugabi, D’Almeida
West Ham United: Trott; Johnson, Pask, Alese (Nebyla 75’), Akinola; Kemp, Makasi, Lewis (Ngakia 65’), Hector-Ingram (Longelo 57’); Chesters, Adarka
Subs not used: Jinadu, Stroud