A new-look Hammers side has endured a tough start to life in the Premier League under Manuel Pellegrini with three straight losses, and its woes continued just minutes into its second round Carabao Cup clash at Wimbledon - the host side taking the lead through Joe Piggot with barely 60 seconds of the match played.
The embattled visitor caught a break midway through the first half when Javier Hernandez was adjudged to have been dragged back while through on goal, leading to a straight red for Wimbledon defender Rodney Macdonald.
Despite being a man up, Pellegrini's team struggled to break down a resilient home side, Issa Diop finally making the breakthrough just after the hour mark, with a swerving shot from outside the area.
Angelo Ogbonna found himself unmarked at a corner and with an easy tap-in to double the lead, before Hernandez capped off a fine team move with a third in stoppage time as West Ham advanced to the third round of the competition, albeit unconvincingly.
Meanwhile Norwegian striker Alexander Soerloth got off the mark for Crystal Palace, latching onto the end of Jairo Reidewald's pass to give his team a 1-0 win over a youthful Swansea City outfit.
Saido Berahino ended a goal drought stretching back 913 days when he opened the scoring for Stoke City in its EFL Cup clash with Huddersfield Town.
The striker turned in a header early in the second half at bet365 Stadium to put his side 1-0 ahead against the Premier League visitor.
It is Berahino's first competitive goal since he scored for West Brom against Crystal Palace in February 2016.
The 25 year-old had played in 48 matches in all competitions since he last found the net.
An own goal to Juninho Bacuna doubled the advantage as Stoke produced the upset of the round to advance past the Terriers 2-0.
In the morning's other major results, Leeds crashed out 2-0 to Preston North End, Aston Villa was stunned by League One struggler Burton Albion, and Norwich City defeated Premier League club Cardiff City 3-1
Other Carabao Cup results:
AFC Bournemouth 3-0 Milton Keynes Dons
Blackburn Rovers 4-1 Lincoln City
Brentford 1-0 Cheltenham
Brighton & Hovre Albion 0-1 Southampton
Burton Albion 1-0 Aston Villa
Cardiff City 1-3 Norwich City
Doncaster Rovers 1-2 Blackpool
Fulham 2-0 Exeter City
Hull City 0-4 Derby County
Leeds United 0-2 Preston North End
Leicster City 4-0 Fleetwood Town
Middlesbrough 2-1 Rochdale
Newport Couty 0-3 Oxford United
QPR 3-1 Bristol Rovers
Sheffield Wednesday 0-2 Wolverhampton Wanderers
Walsall 3-3 (1-3 pens) Macclesfield Town*
Wycombe Wanderers* 2-2 (4-3 pens) Huddersfield Town
West Bromwich Albion 2-1 Mansfield Town