Milivojevic anchors a midfield trio, supporting Michael Olise and Ebere Eze, while the other change sees Jordan Ayew replace Jeffrey Schlupp.
Ayew starts on the right-hand side, with Wilfried Zaha and Odsonne Edouard completing the attack.
It is a familiar back four of Joel Ward, Joachim Andersen, Marc Guéhi and Tyrick Mitchell, ahead of ‘keeper Vicente Guaita.
There are plenty of attacking options on the bench for Palace, with Jean-Philippe Mateta, Malcolm Ebiowei and Schlupp among the replacements.
There is also space in the matchday squad for two Academy prospects, with defender Kofi Balmer and midfielder Killian Phillips included.
Everton: Pickford (GK), Tarkowski, Onana, Calvert-Lewin, Gordon, Gray, Iwobi, Mykolenko, Coleman, Gueye, Coady.
Subs: Begovic (GK), Holgate, Keane, McNeil, Doucoure, Maupay, Davies, Rondon, Garner.
Palace: Guaita (GK), Ward, Andersen, Guéhi, Mitchell, Milivojevic, Eze, Olise, Ayew, Edouard, Zaha.
Subs: Johnstone (GK), Tomkins, Mateta, Schlupp, Hughes, Ebiowei, Balmer, Riedewald, Phillips.