The concession of two early goals ended a below-strength Bohemians' interest in the Cup as a more committed UCD booked their semi-final berth.
Bohemians, with seven changes from the team which won in Galway on Friday, never recovered from poor defending which saw them two goals down within 24 minutes.
The opening goal came on 17 minutes from the unlikely source of Ciaran Kavanagh's head as the diminutive midfielder met an Alan Mahon cross.
A mistake by Brian Shelley then cost Bohemians a second goal within seven minutes.
The young right back, making his competitive debut, lost the ball to Ciaran Martyn, who played a clever one-two with Eoin Bennis to run through and toe-poke the ball past Dempsey.
UCD: Ryan; Mahon, McAuley, Delaney, O'Donnell; Quinn, Lynch, Kavanagh, Martyn; Grogan; Bennis. Subs: O'Byrne for Kavanagh (62 mins), Kilkmurray for McAuley (67 mins), Fitzpatrick for Bennis (75 mins).
Bohemians: Dempsey; Shelley, Maher, Bowman, O'Connor; Fullam, O'Keeffe, Hopper, Williamson; O'Neill, Markey. Subs: Caffrey and Webb for Fullam and Shelley (h-t), Crowe for O'Neill (65 mins).
Referee: H Byrne (Dublin).
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