Young flanker Eoghan Grace helped himself to two tries as Shannon blitzed UCD to move up to second in the table.
Geoff Moylan's side had the game by the scruff of the neck, leading by 26-6 at the interval at Coonagh.
With their pack dominating, Grace and prop Kevin Griffin both touched down and veteran centre Andrew Thompson added another.
UCD full-back Simon Gillespie landed three penalties but Shannon
number 10, Tadhg Bennett, led the scoring with 16 points (try, four conversions and a penalty).
Shannon: Tries: Eoghan Grace 2, Kevin Griffin, Tadhg Bennett, Andrew Thompson; Cons: Tadhg Bennett 4; Pen: Tadhg Bennett
UCD: Pens: Simon Gillespie 3
