Everton striker Kevin Mirallas was the difference with a goal in each half to secure a 2-0 victory.
The Belgian scored the opener, with a side-footed finish from 18 yards, after only six minutes, following some great inter-play between Baines, Fellani and Pienaar.
He then hit the winner only the hour mark after beating Hammers defender Guy Demel and hitting a deflected shot into the top left-hand corner of the net.