The Seagulls had the perfect start with a goal in the second minute when defender Sean Houston headed home from close range after a quickly taken free.
The visitors stretched their lead on 24 minutes. A corner by Dempsey on the left allowed winger Jake Kelly to get in a shot from 12 yards which was flicked home by striker Chris Shields.
The Students might have reduced the lead on the half hour only for Bray ‘keeper Matt Gregg to dive at the feet of striker Graham Rusk.
College did pull a goal back on 56 minutes when a Paul Corry free on the right enabled central defender Michael Leahy to get in a glancing header from close range past Gregg.
Substitute Samir Belhout should have had the Students level seconds later but Gregg got down brilliantly to block his close range effort with the ball rebounding to safety.
Bray wasted an easy opportunity on 72 minutes when substitute John Mulroy headed wide of the target after another teasing corner and Mulroy in added time when his dipping shot from 25 yards was just over the bar.
UCD: Barron; Harding, D.O’Connor, Leahy, Nangle; Marshall (S.Doyle 82), Corry. P.O’Conor, Benson (Belhout 22), Meenan; Rusk.
BRAY WANDERERS: Gregg; S.O’Connor, Mitchell, Prendergast, Houston; McGuinness (Mulroy 64), Dempsey, D.Doyle, J.Kelly (Zambra 58); Shields, Murphy (O’Neill 80).
Referee: Padraig Sutton (Clare).