Bohemians had their noses in front after just nine minutes when a poor David O’Connor clearance was picked up by Ward and the midfielder’s looping shot gave keeper Mark McGinley no chance.
Davy Byrne might have stretched the visitors’ lead on 17 minutes when, after slipping past central defender Hugh Douglas on the left, his angled shot was narrowly off target.
Then Corcoran had a shot just over the top from 22 yards after Karl Moore had carved open the College defence. Little was seen of the students as an attacking force, although striker Graham Rusk did have one long-range effort just wide.
Corcoran scored Bohemians second goal with a magnificent chip into the roof of the net on 52 minutes, after Davy Byrne had created another clearcut opening.
Luke Byrne should have added to the visitors’ tally but blasted over from close range after Karl Moore had expertly prised open the College defence on the right.
The students did have a chance to narrow the gap on 76 minutes only for Chris Lyons to fire in a shot which rebounded off the woodwork, with Paul O’Conor then firing over in a hectic goalmouth scramble.
College did eventually get one on 84 minutes when Derek Pender was adjudged to have taken down Robbie Benson — Rusk making no mistake from the spot.
UCD: McGinley; Langtry, Douglas, D.O’Connor, Nangle; Ledwith, P.O’Conor, Corry; Rusk, Lyons, Morrison (Benson 61).
Bohemians: McNulty; Heary, Mulcahy, McMillan; Pender, Martin, Ward (Traynor 73) , L.Byrne; Moore, D.Byrne (Mahon 66), Corcoran (Buckley 82).
Referee: James McKell (Tipperary).