After the sides' 1-1 draw in the original tie, last week's replay was postponed due to floodlight failure but it was Conan Byrne who provided the spark for the Premier League champions last night.
If Liam Buckley's side are to end their 53-year wait for an FAI Cup title this season, they'll know that better performances will be required further down the line but ahead of a crucial game against Dundalk on Friday, Pat's manoeuvred their way passed a stubborn outfit.
Shels should have opened the scoring inside the opening 10 minutes but after a brilliant solo run, Dylan Connolly shot straight at Brendan Clarke. Conor Murphy did the same with the subsequent rebound. Killian Brennan's free-kick on the stroke of half time was kept out by Greg Murray but Byrne reacted quickest to tap home the rebound - despite the best efforts of the 'keeper.
Murray needed to be alert again shortly after the restart when he brilliantly kept out Chris Forrester's curling effort.
Connolly might have drawn the hosts level just a minute later but his low drive again went straight at Clarke. Forrester should have wrapped up the win late on but he couldn't steer man-of-the-match Keith Fahey's inch-perfect cross passed Murphy - who pulled off a marvellous save.
The impressive 'keeper was called into action again when Fahey's free-kick looked destined for the top corner but he managed to claw it away to safety. But it mattered little as Pat's advance to the quarter-finals where they will meet Bohemians in two weeks.