UCD fittingly ended a run of five straight defeats to honour the tenth anniversary of the death of Dr Tony O'Neill and give their survival hopes a major boost by beating the outgoing champions.
Positive from the start, UCD's early pressure was rewarded with what would prove the game's only goal on 15 minutes.
A Pat McWalters cross wasn't dealt with by either Graham Gartland or Joe Kendrick and Brian King bundled through both and, despite a suspicion of a handball, shot powerfully to the net from 14 yards.
Drogheda sprung to life for the first time on 28 minutes when in-form striker Eamon Zayed, played in by Paul Keegan, put his half-volley wide.
A better chance of an equaliser was wasted on 41 minutes when Zayed's neat touch set up captain Shane Robinson who blasted wide.
College might then have doubled their lead three minutes later, but Alan McNally planted his header over the bar from Shane Duggan's corner.
A brilliant save from Matt Gregg was then needed to deprive Drogheda parity in the final minute of the half when the UCD keeper went full stretch to touch Ollie Cahill's shot onto a post.
Drogheda showed more purpose on the resumption, but it was UCD who should have doubled their lead on 55 minutes. Ian Bermingham's cross ran through for Duggan, but the midfielder sliced his shot off target from a very good position.
Another excellent stop from Gregg deprived Drogheda of an equaliser seven minutes from time, when he saved well from Robinson after Ibrahmia Iyane-Thiam knocked the ball down.
UCD: Gregg; Mahon (Shortall, 62 mins.), Kenna, McNally, Bermingham; King, McFaul (Finn, h/t), Duggan, McWalter; Purcell (Fitzgerald, 90 mins.), Meenan.
Drogheda United: Ewings; Shelley, Maher, Gartland, Kendrick (Ristila, 73 mins.); Baker (Iyane-Thiam, 67 mins.), Keegan, Robinson, Cahill; Zayed, Kuduzovic (Hughes, h/t).
Referee: Derek Tomney (Dublin).
