‘Fabio’ struck with a fine individual effort in the 21st minute, but the Boynesiders were indebted to their keeper Gabriel Sava, who denied the Students on a number of occasions.
Two saves in particular were outstanding, one from Paul Corry and the other to deny Robbie Benson.
Virtually the entire table separated these sides at kick-off and Drogheda were soon in the driving seat, as shots rained down from O’Brien, Eric Foley and Peter Hynes, all of which were comfortably dealt with by keeper Mark McGinley.
UCD looked sharp when coming forward on the counter-attack, but the home side deservedly went ahead on 21 minutes.
Philip Hand swept a free-kick into the box and UCD defender Michael Leahy headed half-clear to the edge of the box, from where O’Brien deftly chipped over McGinley.
The Students responded impressively, however, as David McMillan sent a 30-yard shot flashing wide of Sava’s right-hand post, before the keeper finger-tipped another fine Corry effort onto the crossbar.
Drogheda almost doubled their lead just before half time when a great move involving Cathal Brady and Hynes ended with a Paul Crowley shot that flew a yard wide.
UCD introduced Chris Lyons for Ciaran Nangle at the break and the sub immediately made an impact, turning his man before forcing Sava into a save.
Two minutes later Drogheda were almost caught on the counter-attack when the ball dropped to Robbie Benson 18 yards out and his firm shot was parried brilliantly by Sava at full stretch.
The Students virtually owned the ball for the entire second half against a jaded-looking Drogheda, but other than wayward headers from McMillan and Paul O’Conor they couldn’t find another clear-cut opening.
DROGHEDA UNITED: Sava; McMahon, McNally, Prendergast, Hand; Brady (Mulvenna 68), Crowley, Foley, S Brennan (Marks 65); Hynes (Byrne 55), D O’Brien.
UCD: McGinley; Douglas, Leahy, O’Connor, Ledwith; Belhout, Benson, Corry, O’Conor (McCabe 71), Nangle (Lyons 46); McMillan.
Referee: Tom Connolly (Dublin).