Goals from Showunmi and Andrews, one in each half, saw City home in front of nearly 6,500 fans.
Gary Johnson said afterwards
It was convincing and it was comfortable. Brighton never looked like hurting us when they had the ball and for a while it was a duel between Scott Murray and their keeper.
"Unfortunately, Kuipers won that battle. He has made several great saves to stop us winning by a much bigger margin.
"Our players looked confident and when that happens in football you get performances like that. At times when confidence is not so high you have to stick with players because of what you know they are capable of.
"It's five goals in five games for Enoch and two in two for Wayne Andrews. That's great because you want your strikers to be scoring.
Bristol City: Basso; Orr, McCombe, Carey (Keogh 71), McAllister; Murray, Johnson (Russell 79), Skuse, Myrie-Williams; Showunmi (Fontaine 67), Andrews. Subs not used: Noble, Weale.
Brighton & Hove Albion: Kuipers; Lynch, El-Abd, Butters (Frutos 79), Rents; Fraser (Chamberlain 72), Cox, Hammond, Hart (O'Cearuill 60); Robinson, Gatting. Subs not used: Henderson, Elder.
Goals: Bristol City - Showunmi 41, Andrews 68; Brighton & Hove Albion - none.
Bookings: Bristol City - Andrews (45, unsporting behaviour); Brighton & Hove Albion - El-Abd (22, foul), Hart (45, unsporting behaviour).
Referee: Mr A Bates.
Attendance: 6,485.