Goals from Eddie Gormley and Stephen Fox were enough to see off the Students, and extend Bray's unbeaten run to five games.
Fox opened the scoring for the visitors early in the first half, shooting into the net from a distance from a Keith Long pass.
Alan McNally leveled for the Students mid-way through the first half, but Gormley fired Bray's winner on the half-hour mark with a free-kick.
UCD: B Ryan; Delaney, McAuley, McDonnell; Mahon, Timmons, Doolin, McNally, D Ryan; R Martin, Martyn.
Bray: Young; Long, Charles, Doohan, Farrell; O'Connor, Fox, Morgan, Gormley; Byrne, Keegan.