We are now almost a third of the way through the season and the Hammers are looking good for a top six challenge after an excellent start.
Slaven Bilic's side were looking to bounce back after a poor display in a 2-0 defeat to Watford last time out and Argentine Manuel Lanzini opened the scoring with a superb curling finish into the top corner.
The East Londoners were pegged back by bogey man Romelu Lukaku, though, as he finished off Gerard Deulofeu’s through-ball to secure a point for Roberto Martinez's side.
But how did West Ham's players rate?
Adrian – 6
Neither goalkeeper had too much to do over the course of the 90 minutes. Adrian came rushing out to close down Lukaku as he advanced on goal for the equaliser but the Belgian rounded him before slotting home. The Spanish shot stopper would have been criticised for staying on his line, though, so he was stuck between a rock and a hard place and in this instance the players in front of him let him down for the goal.
Jenkinson – 6
Has turned in much better performances but dealt with the Everton threat well throughout. Had a late effort at goal which was comfortably saved but other than that did not feature enough to make an impact going forwards.
Reid – 6
Almost got a goal late on to win it for the Hammers but the returning centre back probably should have done better than to send his header at the far post over the bar. Was outpaced by Lukaku who split him and James Tomkins expertly to run on to the through-ball for the equaliser but pretty solid other than that one lapse which all came from Dimitri Payet's misplaced pass.
Tomkins – 6
Was not dropped as some had predicted after a poor display and mistake against Watford and did well to contain the Toffees. But like Reid, Tomkins was split and outpaced by Lukaku for the goal, although he won't be the last defender that happens to this season.
Cresswell – 6.5
Almost scored with a very similar effort to Lanzini's with that sublime left foot of his. Other than that, much like Jenkinson, Cresswell on the other flank also struggled to create any chances of note, although he did have more joy getting forward and putting over a few crosses.
Noble – 6.5
Had one of his better games and it was needed as he has been very poor of late. Did not doing anything of any real note, though, and is seen by many fans as a weak link.
Kouyate – 6
A solid enough display but Kouyate's form has dipped slightly of late as well. He has not been his usual rampaging self but still gets through so much work and does the dirty side of the game effortlessly and never shirks his responsibilities.
Moses – 8 – STAR MAN
Comfortably West Ham's best player on the day and if others had been at the same level Bilic's side would have had the win wrapped up. The Chelsea loanee took on Everton defender Galloway at every opportunity and was constantly probing and working his way in and around the box. He went close with a couple of efforts and it was his shot which led to Lanzini's opener. Now he just needs to find that all important consistency as he was pulled off at half-time against Watford for being ineffectual.
Payet – 5
The star summer signing has lit up the Premier League so far this season but this was probably his first poor match so far. He wasn't great at Watford but still played a hand in the key attacking moments at Vicarage Road. Against Everton, despite showing some flashes here and there he didn't influence the match as much as he usually does and after getting a kick from James McCarthy which could have resulted in a red card. He tried to carry on in the second half but came off injured five minutes in.
Lanzini – 7.5
Like Moses Lanzini was always a threat and showed again how crucial he is to this West Ham side. Showed great composure for the goal as he took a touch on the edge of the box picking out the top corner with an ice-cool right-footed finish over Tim Howard.
Carroll – 5
A second start in succession for Carroll replacing the injured Diafra Sakho and another really poor display from the big Geordie. One of the problems against Watford last time out was that Carroll was very isolated up front. And Bilic failed to solve that problem as he faced the same difficulties against the Blues. He was poor all round, though, miscontrolling passes and most of what he did was greeted by moans and groans from the Hammers faithful. Any knockdowns he did make, the midfield were not close enough to him to take advantage.
Zarate – 5
Zarate's 20 minute cameo as a sub for a sub was summed up by the fact he felt he needed to apologise on Twitter for his performance after the game. Fair play to him for admitting he should do better but it was his selfishness that riled West Ham fans, and no doubt his teammates too. Probably trying too hard to impress.
Valencia – 5
Was positive and sent in a dangerous cross after replacing the injured Payet on his second sub appearance since returning from a three-month injury lay-off. But the same fate was to follow for the Ecuardorian just 15 minutes after coming on when he was stretchered off after a hurting the same ankle he injured previously when tackled by Seamus Coleman.
Jelavic – 5
Former Toffee replaced Carroll for the last few minutes but there would be no fairytale goal against his old side as he barely featured.
Subs not used: Randolph, Ogbonna, Antonio, Cullen