Alan Mahon's 84th minute penalty earned UCD a point after Bray produced a fine second half comeback.
Derek Foran's first senior goal for Wanderers helped draw them level to cancel out Pat McWalter's first half opener.
Gavin Whelan then headed in his first goal for the Green and White's but Mahon equalised late on converting a controversial spot-kick.
Shane Fitzgerald went down under Foran's tackle in the box.
Referee Tom Connolly only awarded the 12-yard dead-ball after a flag from his Assistant Fran Cunningham with Mahon sending Alan Gough the wrong way.
Pete Mahon's charges remain without a Premier Division win at the Belfield Bowl this season with their only League success coming at the Carlisle Grounds last March.
But the draw ended Bray's losing streal after suffering back-to-back 30 defeats at the ahnds of Sligo and Cork.
The hosts went in front when Irish U19 left back Ian Bermingham whipped in a 37th minute free which Wicklow native McWalter guided beyond Gough from ten-yards.
But Bray made it 1-1 on the hour.
From Alan Cawley's corner, Kevin Doherty flicked on. And on-loan defender Foran blasted in a left footed half volley from 14 yards.
They then went in front with 12 minutes remaining.
After Ronan Finn conceded a corner, Whelan met Cawley's delivery with a precise front post diving header.
UCD: Gregg; Mahon (Bolger 90 mins), Kenna, McNally, Bermingham ; Fitzgerald, King, Finn (Byrne 80 mins), Doyle; Purcell, McWalter (McMillian 80 mins)
Bray Wanderers: Gough; Ivory, Doherty, Foran, Pender; Whelan, Tresson (McCabe 59 mins) , Cawley, Kavanagh; Dunphy (Onwubiko 59 mins), Rowe
Referee: Tom Connolly (Dublin)
