Goalkeeper Matt Gilks played his part by throwing the ball quickly to the Congolese forward, and although he was fortunate to play a one-two with Kevin Phillips, he strode towards the edge of the box to curl into the top corner past Stephen Bywater.
Green kept West Ham in the match with an excellent save to his left after Odemwingie skipped away from two challenges before attempting to curl in from the edge of the box.
But Everton had other ideas and after they were awarded a free-kick on the edge of area, Baines stepped up to curl a delightful set-piece into Cech's top left-hand corner.