Gary McCabe’s first senior goal saw Bray bring UCD’s 11-game unbeaten run to an end.
The 18-year-old winger turned Alan Mahon and blasted a left-footed drive past Matt Gregg in the 69th minute to give the Seagulls their second win in a row at the Carlisle Grounds.
Andrei Georgescu chased a lost cause to win a corner in the 19th minute from which the Wicklow side took the lead.
From Alan Cawley’s well-flighted delivery, Delaney rose in crowded area to send a six-yard glancing header to the net.
The only other first half chance arrived for the Students in the 37th minute. From Conor Sammon’s break, he played in Derek Doyle whose shot was parried by Steve Williams. The covering Chris Deans headed clear the loose ball in front of goal with Delaney conceding a corner.
Wanderers went close to doubling their lead just 50 seconds after the interval. From Cawley’s short corner to McCabe, Andrei Georgescu headed wide at the back post.
Straight away, the visitors broke down the right. The ball was not cleared from Conan Byrne’s centre and Derek Doyle pounced with a low 12-yard finish.
Bray Wanderers: Williams; Tresson, Deans, Delaney, Cronin; O’Shea, Cawley (Caffrey 69 mins), Duggan, McCabe; Fox (Derek Tyrrell 89 mins), Georgescu (Dunphy 84 mins).
UCD: Gregg; Mahon (Forsyth 86 mins), Kenna, McNally, Bermigham; Conan Byrne, McFaul, Shorthall (Bolger 63 mins), Doyle; Sammon (Purcell 80 mins), Paul Byrne
Referee: Derek Tomney (Dublin).