It will be Moyes' first derby in charge since succeeding Sir Alex Ferguson.
Zabaleta said: "It's a special game, one in which everyone wants to play and one the fans want to watch and to celebrate. It won't be any different - even without Fergie they are still Manchester United.
"Ferguson was a great manager and an important person for the club.
"But now it is a different part of history and we have to respect David Moyes because he is the new manager. It was always tough for us to beat Everton when David Moyes was there."