The three-time competition winners last tasted success in 2012 and after relinquishing their crown last year, the Glasnevin-based outfit are keen to get back to the summit.
Dublin’s McHugh was the star of the show with 1-5 while Wicklow’s Conor McGraynor notched 1-2.
Three first half goals provided the platform for a comprehensive, if flattering, victory in a fixture that was switched to Blanchardstown.
NUIG opened brightly and led by 0-3 to 0-0 early on, with Shane Moran adding to early frees from Johnny Kelly and Adrian Varley.
Ultimately, however, NUIG would suffer from an inability to breach the DCU defence.
NUIG managed just 0-3 from play during the game as Kelly and Varley converted eight frees between them.
And that was never going to be good enough against a DCU side that took four of the numerous goal chances they created.
Longford star Michael Quinn smashed home the opener in the 16th minute and while NUIG pulled level at 0-7 to 1-4, McGraynor and McHugh raised green flags to establish a 3-6 to 0-8 interval lead.
The second half turned into a procession for DCU and the fourth goal arrived in the 39th minute.
NUIG had already lost Sean Moran to a black card early in the second half and corner back Adrian Nolan suffered a similar fate when he dragged down McHugh.
From the resultant penalty, Gary Kelly made no mistake and DCU advanced to the last eight and a mouthwatering date with UCD.
Scorers for DCU: C McHugh 1-5, C McGraynor 1-2, G Kelly 1-1 (1-0 pen), M Quinn 1-0, B Donnelly 0-3 (2 45s), S Oates 0-2, C Cafferky & D Byrne 0-1 each.
Scorers for NUIG: A Varley 0-6f, D McCormack 0-2, J Kelly 0-2f, Shane Moran 0-1.
DCU: J Farrelly (Cavan); E Murray (Galway), D Wrynn (Leitrim), C Cafferky (Roscommon); P Dooney (Monaghan), C Dunleavy (Dublin), F Kelly (Roscommon); E O’Connor (Louth), B Donnelly (Louth); M Quinn (Longford), P Fox (Meath), D Byrne (Dublin); C McHugh (Dublin), C McGraynor (Wicklow), G Kelly (Galway).
Subs: G Sweeney (Dublin) for Dunleavy (26), C Compton (Roscommon) for Fox (h.t), S Oates (Roscommon) for Kelly (40), F O’Shea (Cork) for Dooney (43), T Flynn (Galway) for Quinn (50), C Moynagh (Cavan) for Donnelly (50).
NUIG: D O’Sullivan (Limerick); A Nolan (Galway), C Crowe (Mayo), L Cullen (Fermanagh); C O’Domhnaill (Galway), J McManus (Roscommon), D Gavin (Mayo); Shane Moran (Leitrim), E O’Heochaidh (Galway); J Kelly (Sligo), Sean Moran (Galway), D Comer (Galway); D McCormack (Westmeath), A Varley (Galway), K Reilly (Westmeath).
Subs: K Gibbons (Mayo) for O’Domhnaill (h.t), C Guckian (Leitrim) for Sean Moran (black card, 31), S Gaffney (Galway) for Nolan (black card, 38), I Galvin (Kerry) for O’Heochaidh (52).
Referee: P Hughes (Armagh).