The Hammers beat Tottenham Hotspur 1-0 at Upton Park on Tuesday night, taking them to just one point behind fourth placed Manchester City.
It's been a stunning debut season for manager Slaven Bilic, who is now challenging for Champions League qualification, and can move one step closer to that stunning achievement with a win against Everton this afternoon.
The Toffees will wish that it was they who were challenging for the top four, but they are instead languishing in mid-table under manager Roberto Martinez.
Despite having a host of superb players like John Stones, Ross Barkley, Gerard Deulofeu and Romelu Lukaku, Everton have struggled to hit top form this season, with their home form a particular concern.
Now, Bilic - a former Everton defender - heads back to Goodison Park in search of a win that would pile more pressure on Martinez, but pundit Mark Lawrenson believes the game will end 1-1.
Speaking to BBC Sport, Lawrenson suggested that Hammers midfielder Mark Noble deserves far more praise, and thinks West Ham deserve to be talked about more as the race for the top four places hots up.
"West Ham's season keeps getting better and better and I think they are as fit, strong and athletic as any team in the league," said Lawrenson. "We know that because they keep coming back in away games when they have been under the cosh, and they have got some unsung players in their squad - Mark Noble never gets the credit he deserves."
"It is a boost for the Hammers that Diafra Sakho is on his way back to full fitness but they are short of available centre-halves, so losing James Collins to a hamstring injury is a big blow. Despite beating Tottenham on Wednesday, West Ham are not getting any mentions when it comes to the title race. I don't think they are going to win it but they have put themselves in the frame for the top four."
"Everton, in contrast, are stuck in mid-table at the moment but they can still climb the table too, and that would certainly help attract players if they look to spend big in the summer," he added.
What's your prediction for Everton v West Ham?