Bright start for Horton.
The former Brighton midfielder and Manchester City boss saw his side come from behind and then hold on for a crucial victory.
Flitcroft fired Chester ahead in the first ten minutes, neatly steering the ball in from Wood's cross.
Brighton hit back on the half-hour, with Mayo drilling in a sweet left- foot volley.
Ansah's second goal of the week put the home side ahead just before the break.
In the second half Mayo hit another beauty when he converted Storer's cross for his fourth goal of the season.
Murphy gave Chester hope when he pulled a goal back, but despite facing frantic late pressure Brighton hung on to claim the three points.