For a long time it appeared Paul Lambert's side would be celebrating their second surprise success on Merseyside, having beaten Liverpool in December.
But Fellaini scored his second of the afternoon to add to Victor Anichebe's first-half strike and cancel out Christian Benteke's double and a goal from Gabriel Agbonlahor.
Conceding in the second minute lead was disappointing for Everton. John Heitinga was culpable as Benteke went past him as if he were standing still to slide a shot across Tim Howard from Charles N'Zogbia's pass.
Benteke continued to look threatening and his shot from Agbonlahor's cutback was deflected behind before Everton drew level thanks to their own powerhouse forward as Anichebe scored a 21st-minute equaliser.
Having held up Kevin Mirallas' pass by using his superior upper body strength, he then turned Ciaran Clark to fire a left-footed shot past Bradley Guzan for his fifth goal in eight league starts.
Heitinga, who has not enjoyed the best of seasons, was again involved in Villa's second. A corner was only partially cleared and Ashley Westwood's right-wing cross saw Agbonlahor lose the Holland international and outjump Fellaini to head in at the far post.
Villa should have put the result to bed in the second half when Agbonlahor played in Andreas Weimann but the Austrian blazed well over with only Howard to beat. He made up for it with his involvement in the third goal, which saw him exchange passes with Matthew Lowton, who crossed for Benteke to nod in at the near post.
With 20 minutes to go, Fellaini cut in from the left and again utilised Anichebe's strength to hold up the ball before taking the return pass to shoot past Guzan with the help of a minor deflection.
Nikica Jelavic had one shot batted away by Guzan but the form guide appeared to be against the Toffees. But Fellaini's header in the third of six added minutes changed that and the Belgium international could have won it even later but shot straight at the goalkeeper.
- Sports & Recreation
- Gabriel Agbonlahor
- Christian Benteke
- Victor Anichebe