The visitors, managed by former Treaty boss Liam Kearns, led 0-2 to 0-1 early in the game after Kerry star James O’Donoghue scored the first of his four points at the Dub in Belfast.
However, once Queen’s got in front, reeling off the next four points, they managed to stay ahead for most of the game.
Donegal’s All-Ireland winner Martin McElhinney dispossessed his marker and scored the first of Queen’s four unanswered points while Ryan Rafferty got two in two minutes as they raced into a 0-5 to 0-2 lead after 19 minutes.
Although they were chasing the game for long spells, UL hung in and had their best spell either side of half-time. They started to win more breaks around midfield which gave them a platform to attack. JP Spillane and David Dolan both scored from play, Dolan’s brilliant curling effort from 35 yards just before half-time bringing UL to within a point of Queen’s, 0-6 to 0-5, at the break.
Rory Grugan stretched Queen’s lead 20 seconds after the restart but UL briefly drew level at 0-7 apiece in the 37th minute through Shane O’Callaghan’s point.
Queen’s went on another four-point scoring burst, with Darren O’Hanlon, Ryan Murray, Ryan Jones and the impressive Ryan Mallon all on target.
UL showed great persistence, however, and, despite dropping a few shots short, a James O’Donoghue brace and a fine score by Denis Daly brought them within a point again.
However, Mallon was the most influential player on the field in the closing stages and helped Queen’s through to next week’s home tie against GMIT.
Scorers for Queen’s: R Mallon, R Rafferty, R Grugan, R Murray 0-2 each, P Quinn, D O’Hanlon, C McCartan, M McElhinney, R Jones 0-1 each
Scorers for UL: J O’Donoghue 0-4 (2f), B O’Shea 0-3 (3f), D Dolan, D Daly, S O’Callaghan, JP Spillane 0-1 each
QUEEN’S UNIVERSITY: M Cunningham (Down); P Quinn (Derry), C Cullen (Fermanagh), C McNulty (Tyrone); R Mallon (Down), D O’Hanlon (Louth), C McCartan (Down); M McElhinney (Donegal), H Og Conlan (Tyrone); C Maginn (Down), R Grugan (Armagh), R Jones (Fermanagh); G Collins (Down), N McKenna (Tyrone), R Rafferty (Armagh)
Subs: R Murray (Antrim) for Collins (HT), S McArdle (Down) for Jones (48), R McGarry (Down) for Rafferty (50), R Jones (Fermanagh) for Conlan (60)
UNIVERSITY OF LIMERICK: R Byrne (Mayo); E Kiely (Kerry), T Clancy (Cork), B Harrison (Mayo); D Dolan (Mayo), J O’Rourke (Cork), L Mulligan (Kerry); P McHugh (Leitrim), C McNamee (Offaly); JP Spillane (Kerry), D Daly (Kerry), E Carroll (Offaly); S O’Callaghan (Kerry), J O’Donoghue (Kerry), B O’Shea (Kerry)
Referee: Barry Cassidy (Derry)