George Hirst scored twice at LCFC Training Ground, either side of Tawanda Maswanhise adding his name to the scoresheet once more for the side coached by Ben Petty, while Pierre Ekwah was on target for the visitors.
Making three switches from the side that lost out to Manchester City, the Foxes youngsters fielded Callum Wright and Hirst for the first time this term, as well as Joe Wormleighton, replacing Iestyn Hughes, Shane Flynn and Ethan Fitzhugh.
Hirst was right in the thick of the action within six minutes of kick-off. The hosts had already gone close when captain Lewis Brunt saw his effort from Sammy Braybrooke's corner hooked off the line, and they made the breakthrough shortly after.
Wanya Marcal-Madivadua drove towards the byline, cutting back onto his left foot to cross for Maswanhise, whose effort came back off the post, but his forward partner was there to finish first-time.
The visitors looked to respond from Regan Clayton’s corner, which was met by Ekwah, though Chituru Odunze managed to comfortably hold on.
The American shot-stopper was soon able to deny Kamari Swyer’s header from close range, from Will Greenidge’s cross, and, called into action again, kept out a low shot from Ademipo Odubeko.
Having weathered that storm, City doubled their advantage on 25 minutes. Maswanhise emphatically volleyed home Wormleighton's centre, which was sent in off the underside of the bar.
The away side battled away, halving the deficit within seven minutes, courtesy of a sensational hit from Ekwah, who robbed Braybrooke of possession on the edge of the box before looping the ball over Odunze and into the roof of the net.
That gave West Ham a lifeline and it could have been all square had Ekwah beaten Odunze again when he worked the ball onto his left and struck a low drive that the 'keeper managed to tip round the post.
Leicester regained momentum as the half came to a close and might have stretched the advantage had Hirst kept his header down from a Will Alves cross, instead diverting it onto the roof of the net.
The Hammers started the second period showing intent, with Dan Chesters’ attempt hitting the side netting. A wake up call for City, they soon went on the attack themselves via Marcal-Madivadua, flashing a left-footed shot narrowly wide of the post.
The winger then drove inside but got the shot all wrong from the edge of the area, before Kasey McAteer forced Krisztian Hegyi into a smart save.
It then turned into an open encounter, with both sides desperate for the next goal. Firstly Ademipo Odubeko could not find the target for the away side, before Hirst headed just over the bar at the other end.
Greenidge was next to try his luck, striking wide for West Ham after Chesters went down in the area appealing for a penalty.
But it would be Leicester who grabbed that all important fourth goal of the evening. Marcal-Madivadua kept the ball alive at the back post, flicking it back for Hirst to strike on the turn and net his brace.
The forward, on loan at Portsmouth last season, was in the mood for more and soon sent a fierce shot towards goal that Hegyi did well to stop, though that was Hirst's last action.
Marcal-Madivadua then combined with substitute Fitzhugh, who blazed over the bar, giving the Hammers a glimmer of hope for an unlikely comeback.
That faded when Keenan Appiah-Forson failed to hit the target when played in, finding the side netting, and City kept their two-goal lead.
Major moment – The third goal
After such an impressive start, netting twice in 25 minutes, the Foxes might have been rocked by West Ham getting one back. The third, Hirst's second of the evening, largely calmed any such nerves and they were able to see out a comfortable victory.
Who impressed? – A host of good performances
Co-commentator Gerry Taggart on LCFC TV: "It's been a really solid display. The more experienced players have played a part in that. Wright, Hirst and Maswanhise - it was a fantastic performance from him. Brunt was solid and looks head and shoulders the best player on the pitch for me. Braybrooke just controlled the midfield and showed the true quality he's got in the last move."
Where do we stand? – Sixth position
Leicester rise up to sixth in Premier League 2 Division 1, on four points from three games at this early stage of the season.
Coming up – Blackburn Rovers (A)
Blackburn Rovers Under-21s are the next challenge for City's youngsters, facing the Lancashire side at Lancashire FA on Saturday 27 August (12pm BST kick-off).
The details...
City: Odunze; Appiah, Brunt (c) Wormleighton; Marcal-Madivadua, Braybrooke, Alves (Ewing 53'), McAteer; Wright (Fitzhugh 65'); Maswanhise (T. Pennant 74'), Hirst (K. Pennant 74').
Sub not used: Doherty.
Goals: Hirst 7’, 66', Maswanhise 25'.