The home side got off to a dream start with a goal from Conor Laverty after 55 seconds.
Down’s Caolan Mooney scored a superb point for the students in UU’s only score from play in the first half.
Mayo star Cillian O’Connor converted tricky dead ball chances into a difficult wind as UU trailed by 1-5 to 0-3 at the break.
Niall McKeever was credited with a bizarre goal for UU after 41 minutes.
Down pulled clear in the last 10 minutes with scores from Cathal Crilly and Conor Laverty to ensure victory.
DOWN: S Kane; D O’Hagan, L Howard, D Turley; M Magee, B McArdle, D McKay (0-1); N Madine (0-1), P Fitzpatrick (0-1); P Devlin (0-2, 2f), C McGovern, C Maginn (0-1); C Laverty (1-1), A McConville (0-1), D O’Hare (0-4, 2f).
Subs: C Garvey for McKay (HT), K McKernan for D Turley (54), P Turley for Madine (BC, 57), C Crilly (0-1) for McGovern (62), K Anderson for McConville (66)
UU: S Fox; K Brady, R Johnston, D McNally; B Sankey, M Donnelly, C Harkin; C Mooney (0-1), N McKeever (1-1); F Burns, C O’Boyle, R Donnelly; L Gervin, R O’Neill, C O’Connor (0-3, 3f).
Subs: P McBrearty (0-2) for Gervin (HT), K Hughes for Harkin (HT), M Johnston for Sankey (47), P Casey for McNally (53), J McGovern for Burns (68), R McAlinden for R Donnelly (68)
Referee: Sean Laverty (Antrim).