However, Premier League Cardiff City were dumped out 3-1 by second-tier Norwich City, while Southampton won 1-0 in an all-top-tier tie at South-Coast rivals Brighton & Hove Albion.
West Ham had lost their first three Premier League games to sit bottom of the table and their dismal start to the campaign had already sparked speculation among pundits as to whether new manager Manuel Pellegrini would see out the season.
Things took a turn for the worse for the East London club when Joe Pigott put Wimbledon ahead with a powerful header after two minutes and the sending off of the hosts' Rod McDonald after 18 minutes did not immediately improve the visitors' fortunes.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
While West Ham pressed for an equaliser they had to wait until the 63rd minute for centre back Issa Diop to drive in a leveller before Angelo Ogbonna tapped in to deflate home hopes and Javier Hernandez rounded off the scoring in stoppage time.
There was no fightback for Cardiff who rested players at home to Norwich and paid a heavy price.
Dennis Srbeny scored twice to put the visitors 2-0 ahead and Maximillian Aarons added to their lead before Bruno Manga scored a late consolation goal for Cardiff.
Charlie Austin grabbed the winner for Southampton after 88 minutes at Brighton, while Leicester City thumped third-tier Fleetwood Town 4-0 with Christian Fuchs and Rachid Ghezzal scoring stunning goals for the hosts.
Vicente Iborra and Kelechi Iheanacho were also on the scoresheet for the Foxes.
Stoke City's Saido Berahino scored his first club goal in 913 days as the second-tier side beat Premier League Huddersfield Town 2-0, while top flight Crystal Palace won 1-0 at Swansea City with a close-range finish by Alexander Sorloth.
Bournemouth maintained their unbeaten start to the season with a 3-0 win over League Two MK Dons while Aboubakar Kamara scored twice as Fulham beat fourth tier Exeter City 2-0.
The four remaining ties will be played on Wednesday.
(Reporting by Toby Davis; Editing by Ken Ferris)
