Lukas Nmecha put City in front with a penalty, before second-half substitute Raheem Sterling scored twice.
Pep Guardiola’s side will face Wolves in the final on Saturday (12:30 BST).
West Ham started brightly and took a deserved lead when veteran midfielder Noble converted from the spot, after Felipe Anderson was brought down by Angelino.
The City left-back was fortunate not to concede another penalty moments later when he was involved with a challenge with Ryan Fredericks, but City regained their composure.
New signing Rodri and impressive youngsters Nmecha and Tommy Doyle began to have a greater iNFLuence as Silva controlled Adrian Bernabe’s pin-point cross with his chest before firing the equaliser past West Ham’s new goalkeeper Roberto.
Nmecha then won and scored his own penalty to hand City the lead, but Guardiola introduced several more experienced players from the bench after the interval.
Substitutes Leroy Sane and Sterling combined for the latter’s first goal before the England international added his side’s fourth.
The Hammers, who will play Newcastle in Steve Bruce’s first game as Magpies manager in the third/fourth play-off on Saturday, went close to finding a late consolation goal through Andriy Yarmolenko, but the striker could not convert from close range after ClAudio Bravo parried Javier Hernandez’s direct free-kick.