Graham then appeared set to double Swansea's advantage before half-time but Ward's intervention nicked the ball off his toe as he waited for a tap-in at the far post.
Again Bellamy was the creator as his low pass across the six-yard box, after a neat one-two with Simon Davies, found Ledley unmarked at the far post for a simple tap in.
Two minutes later Everton were ahead when Baines picked out the distinctive mop-haired figure of Fellaini with a low ball from the left leaving the Belgian with a tap-in at the far post.