The Hammers and their beleaguered manager Avram Grant seemed on course for victory at Goodison Park as Frederic Piquionne headed them in front for the second time six minutes from time.
But Piquionne was sent off for celebrating with fans and the Hammers, who remain bottom of the Barclays Premier League, were denied as Fellaini struck.
The visitors had taken the lead after 27 minutes as the once goal-shy Jonathan Spector found the net for the fourth time in two months but Diniyar Bilyaletdinov came off the Everton bench to level.
The result was yet another blow for Grant, whose position has again been the subject of heavy speculation over the past week.
Source: PA
Source: PA