The Toffees head to Upton Park full of confidence following their win over Chelsea last time out, while the hosts have injury problems and are struggling for goals
Bobby Zamora's first-half effort was enough to give West Ham a 1-0 victory on that occasion, but they have lost six and drawn four of the 10 Premier League encounters between the teams since then.
The match marks Hammers manager Sam Allardyce's 100th game in charge of the London club, and the former Blackburn Rovers boss will be desperate to see his side's lean spell in front of goal end.
After starting the campaign with an opening-day 2-0 victory over Cardiff City, east Londoners have failed to score in their last three games.
The Upton Park outfit have not gone four games without registering since October 2006, and Allardyce admits his side's barren run is a concern.
"Yes [the lack of goals is worrying], there's no doubt about it," he told reporters. "We've been creating chances but our quality of finishing has not been good enough.
"Opportunities have arisen for us and although we took them very well against Cardiff, we've been unable to take them in the other games."
West Ham's struggles in front of goal have not been helped by the absence of striker Andy Carroll, who remains on the sidelines with a foot injury, while Joe Cole (hamstring), Stewart Downing (leg), Alou Diarra (knee) and George McCartney (knee) will also miss out.
Roberto Martinez's Everton meanwhile head into the fixture buoyed by their 1-0 victory over Chelsea at Goodison Park last time out, which continued their unbeaten start to the season.
Steven Naismith's close-range header on the stroke of half-time was enough to hand the Spaniard his first Premier League triumph for his new club.
But the former Wigan Athletic manager warned his side not to be complacent, and to be particularly aware of West Ham's threat at set pieces.
"It's important we understand that West Ham have got a really strong unit," he told Everton's official website.
"We are well aware of the quality and goalscoring ability they have in dead-ball situations."
Martinez could hand striker Romelu Lukaku his debut after his deadline day loan move from Chelsea, while midfielder Darron Gibson and forward Arouna Kone (both knee) are set to return to the squad.
But Steven Pienaar and Antolin Alcaraz continue to struggle with hamstring injuries - the former is rated as "50-50" for Saturday by Martinez, while the latter is definitely unavailable.