Aston Villa's Hourihane has been handed a spot in midfield, while Brentford defender Egan will start at centre-back alongside Alex Pearce.
As for Iceland, Cardiff City midfielder Aron Gunnarsson will captain a team that shows seven changes from their 2-1 win over Kosovo on Friday night.
Republic of Ireland: Westwood; Christie, Pearce, Egan, Brady; McGeady, Hendrick, Hourihane; Hayes, Doyle, McClean
Subs: C. Doyle, Keogh, Gleeson, Ward, Meyler, Long, Boyle, Horgan, O'Dowda, O'Kane
Iceland: Kristinsson; Saevarsson, Ingason, R.Sigurdsson, A. Sigurdason, Bodvarsson, O. Skulason, Gunnarsson, Magnusson, Gisalon, Finnbogason
Subs: Halldorsson, I. Jonsson, Ari Jonsson, Eyjolfsson, Omarsson, Kjartansson, Karlsson, Arnason, Smarason, B. Sigurdarson, A.Skulason