The first, and one of the only first-half chances for the visitors, came after five minutes when Lucas Neill's outswinging corner found James Tomkins rising in the box, but the young central defender could only hit the bar on his debut for the club.
Everton then dominated the next 40 minutes, but they took the lead after only eight when a long punt upfield by Tim Howard was flicked on by Victor Anichebe to strike partner Yakubu.
The Nigeria international out-muscled three Hammers defenders before smashing home his 19th goal of the season past Robert Green.
The Blues pounded the visiting side and chances for Leon Osman and Anichebe had Alan Curbishley's men camped in their own half.
Everton should have doubled their lead in the 15th minute when Anichebe fought his way to the edge of the box and, after Scott Parker had made the tackle, the ball went straight to Yakubu who put the ball in the back of the net only to be wrongly flagged offside.
Against the run of play, West Ham should have equalised just after the half-hour mark through Dean Ashton. An uncharacteristic mix-up between Mikel Arteta and Phil Jagielka led to the big striker having a clear shot at goal but the former Crewe and Norwich hit-man could only drag his effort wide.
With no other strikers on the bench, David Moyes was forced to pair Yakubu and Anichebe together, but the two big forwards linked up well and Anichebe probably should have scored on 41 minutes.
A neat ball from the goalscorer split the Hammers defence but an onrushing Green spread himself well to deny the young forward.
Having not been tested for nearly the whole of the first half, Howard make a smart save with his foot to deny Ashton just before the interval.
The stocky centre-forward rifled in a 25-yard shot and a deflection off Joleon Lescott's knee sent the ball away from a diving Howard but the Blues' shot-stopper reacted well to save the ball on the line with his trailing foot.
The home side set about the second half searching for the all-important second goal and efforts from both forwards were saved by Green who was in top form as he kept his side in the game.
It took just over an hour for West Ham to start carving out chances of their own as the visitors started to pile on the pressure and an equaliser looked only a matter of time.
Mark Noble's free-kick sailed just over the bar and Freddie Ljungberg's effort was saved by Howard.
However, the chances kept coming and finally Curbishley's men found the back of the net when a deep cross by captain Neill found Ashton who powered a 68th-minute header home.
Everton lost all their momentum and were totally outplayed for the last third of the game and Moyes may feel it is a point gained after young substitute Freddie Sears almost scored in the final minute.
The teenager skipped past Jagielka and side-footed the ball past a stranded Howard only for it to roll against the foot of the post and come straight back out.