Villa took only four minutes to open their account when John McGinn picked out Grealish after Fulham failed to clear their defensive lines and the playmaker slotted the ball home.
The visitors doubled their advantage 11 minutes later. McGinn was again the provider, this time finding Hourihane whose right-foot shot was beyond goalkeeper Alphonse Areola.
Tyrone Mings extended Villa's lead just after half-time, steering home Hourihane's free-kick.
Bobby De Cordova-Reid had a 56th-minute close-range effort ruled out following a VAR review and Aleksandar Mitrovic twice went close with headers but there was to be no way through for the hosts.
Fulham remain without a point and are at the foot of the table while Villa have won both of their opening matches.
Budweiser King of the Match: Jack Grealish
Fulham: 4 Oct v Wolves (A)
Aston Villa: 4 Oct v Liverpool (H)