The Hammers netted three goals in the final half-hour, two of those in the closing 10 minutes, to pick up their first win of the season at the fourth attempt after Joe Pigott gave the Dons a second-minute lead.
A red card shown to Rod McDonald 18 minutes in made the task of holding on all the more difficult for the League One hosts, and so it proved as defenders Issa Diop and Angelo Ogbonna found a way through to prevent an upset, before Javier Hernandez added a late third.
West Ham, showing nine changes from their 3-1 loss at Arsenal, should have been level 15 minutes in, only for Andriy Yarmolenko - making his full debut alongside Lucas Perez - to sky over the bar from seven yards.
United's quest to find a route back into the game was boosted just a under a quarter of the way through when centre-back McDonald picked up two yellow cards in quick succession, the second for a pull on Hernandez's shirt 19 yards out.
The opportunities kept on coming for the Hammers, with Hernandez glancing a cross wide and Robert Snodgrass looping one into the hands of a grateful King.
Wimbledon survived a scare right at the end of the first half when Will Nightingale, brought on for goalscorer Pigott as Neal Ardley sacrificed a striker, stopped Yarmolenko's header right on the line.
Manuel Pellegrini took off holding midfielder Obiang at the break and brought on another attacker in Felipe Anderson, but it was proving to be a familiar story in the opening 15 minutes of the second period.
All United had to show for their dominance was a couple of Hernandez efforts on target from inside the box, both of which King easily dealt with, and Anderson also sent a long-range drive into the side-netting.
The leveller arrived just after the hour, though, as Diop carried the ball forward and thumped it past King from 25 yards after being given too much time and space.
Hernandez then miscued a good opportunity to put his side ahead, shortly after Diop had powered a header against the crossbar at the end of a corner.
With 85% of possession to their name as the game entered its final 15 minutes, the pressure finally told as West Ham snatched a late winner through Ogbonna.
The centre-back stuck out a leg to convert Snodgrass's deep corner at the back post, and two became three before the full-time whistle sounded thanks to Hernandez's smart finish after latching on to a long ball.
AFC WIMBLEDON (4-4-2): King; Sibbick, Garratt, Oshilaja, McDonald; Pinnock (Wordsworth 68'), Hartigan, Trotter, Wagstaff; Hanson (Appiah 79'), Pigott (Nightingale 36')
WEST HAM UNITED (4-2-3-1): Adrian; Zabaleta, Diop, Ogbonna, Cresswell; Rice, Obiang (Anderson 46'); Yarmolenko (Masuaku 90'), Snodgrass, Lucas Perez (Antonio 81'); Hernandez