One of the weekend's controversial handball decisions aided Carlo Ancelotti's Toffees in their 2-1 victory over Crystal Palace at the weekend, but David Moyes' Hammers needed no such good fortune. A comprehensive 4-0 thrashing of Wolves shocked even their own supporters and the east Londoners will be looking to build on that impressive result.
With a condensed season expected to cause severe fixture congestion for the league's traditional 'big six', the likes of Everton and West Ham may not have a better chance to win a domestic trophy for many years.
Where to Watch on TV
When Is Kick Off? Wednesday 30 September
What Time Is Kick Off? 19:45 (BST)
Where Is it Played? Goodison Park
TV Channel/Live Stream? Sky Sports Main Event (UK)
Referee? Darren England
Centre backs Jarrad Branthwaite and Mason Holgate remain sidelined through injury, so Michael Keane is expected to partner Yerry Mina in the heart of defence once again.
Jordan Pickford has come under criticism of late, especially for his blunder in the last round of the Carabao Cup against Fleetwood Town, so Jonas Lossl could come in to replace him after returning to the Everton bench at the weekend.
Ancelotti has a host of fringe players who will be hopeful of getting minutes under their belt in this midweek encounter, with the likes of Gylfi Sigurdsson, Theo Walcott and Moise Kean pushing for starts.
Sebastien Haller is the top scorer in the Carabao Cup so far with an impressive four goals in just two matches. The £45m striker made the switch to the London Stadium last season but struggled in his maiden campaign. However, he's started the new season like he has a point to prove.
He'll likely form an attack alongside Andriy Yarmolenko and Felipe Anderson as the Ukraine international steps up his recovery from injury and the Brazilian winger looks to rediscover his best form.
Ryan Fredericks picked up a hamstring problem just three minutes into the second half against Wolves so won't be available for this one, while Josh Cullen and Issa Diop remain in self-isolation after testing positive for Covid-19.
Everton: Pickford; Kenny, Mina, Keane, Digne; Davies, Sigurdsson, Doucoure; Iwobi, Calvert-Lewin, Bernard.
West Ham: Randolph; Johnson, Balbuena, Ogbonna, Masuaku; Noble, Rice; Yarmolenko, Lanzini, Anderson; Haller.
Everton have had the perfect start to the new campaign. They've recorded three consecutive victories in the Premier League, achieving maximum points in the early stages of a season that appears to hold a lot of promise. Their new big-money signings have settled into life in England well, although it's unlikely all of them will start against West Ham.
The Goodison Park side have scored eight goals in the last two rounds of the Carabao Cup, dispatching Salford and Fleetwood Town respectively.
Moyes' men have matched Ancelotti's for goals scored so far in the competition by putting three past Charlton and then five past Hull. They seem to have recovered from a disastrous opening day defeat to Newcastle with a good performance against Arsenal before their victory over Nuno Espirito Santo's much-admired Wolves.
Here's how the two sides have fared in their last five fixtures...
Crystal Palace 1-2 Everton (26/9)
Fleetwood 2-5 Everton (23/9)
Everton 5-2 West Brom (19/9)
Everton 3-0 Salford (16/9)
Tottenham 0-1 Everton (13/9)
West Ham 4-0 Wolves (27/9)
West Ham 5-1 Hull City (22/9)
Arsenal 2-1 West Ham (19/9)
West Ham 3-0 Charlton (15/9)
West Ham 0-2 Newcastle (12/9)
It should be a close affair, with both teams confident after their most recent results and keen to advance into the later rounds of this competition.
Both sides have relatively good strength in depth in the attacking areas but less so at the back, meaning it could be a high scoring affair. Everton have more momentum and home advantage - although that is lessened in the current climate - and should have enough to see them through to the fifth round.
Prediction: Everton 3-2 West Ham