The Toffees travel to the Stadium of Light still in the chase for Champions League places while the Black Cats are in trouble at the opposite end of the Barclays Premier League.
Everton remained four points behind fourth-placed Arsenal after drawing with the Gunners in midweek and, with five games left, can still force their way in.
Sunderland, although apparently rejuvenated by the arrival of Paolo Di Canio as manager, are still just three points above the relegation zone.
Moyes said: "Our need is as great, from our point of view.
"We have got to keep winning and we will have to try that again at Sunderland.
"When people are asking me if we are still in the hunt for Europe, I am pleased about that."