Everything seemed to be going according to plan for the favourites, who with wind assistance, enjoyed a five-points cushion at the break. That was down mainly to the dead eye accuracy of Offaly senior Brian Carroll who finished the day with 0-11 eight from placed balls.
They seemed certainties to advance when the conditions calmed and, with 20 minutes to play, St Pat's had only managed to chisel away a single point of the deficit.
Yet slowly and surely, the gap began to narrow until, with five minutes to go, a point from Kilkenny's Joe Herrity brought the hosts on level terms.
Unfortunately for Pat's, they had left little or nothing in the tank in their efforts to recover the lost ground and when they put their foot to the throttle for the run-in they simply spluttered to a halt.
UL eventually recovered their composure to reel off four points before the final whistle which secures a second round tie against UCD in six days' time.
Yesterday's scrape will have given them much to consider. When Pat's began to turn the screw, UL failed to score from play for 20 minutes and only Carroll's effort kept them ahead.
Alan Egan was the only UL forward apart from Carroll to land more than one point and three of his came within a lightning three minutes after the throw-in.
That was the fuse that sparked UL's first-half dominance but the platform was built largely on the half-back and midfield lines that consistently smothered the Dublin side's attacking ambitions while setting their own in motion.
Though Pat's spread the scoring duties better, they will rue their first-half when only Richie Power's dead ball prowess kept them within touching distance. Their first score from play didn't materialise until his Kilkenny compatriot Mark Walsh pointed four minutes before the change of ends.
ST PATS: D O'Brien; D Kelleher, M Heffernan, J Robinson; E Bulger, P Hogan (0-1), B Dillon (0-1); D Herity (0-3), F Lyons; M Walsh (0-1), M Doyle, R Power (0-5, 3f); G Arthur, C Doyle, E O'Donoghue (0-4, 3f).
Subs: D O'Neill for Doyle 24.
UL: T Flynn; A Murphy, P Dowling, T Gilternane; R Hayes, B Bulger, B Coleman; T Stapleton (0-1), P Donnellan (0-2); T Healy, J Green (0-1), N Kenny; G Ryan, B Carroll (0-11, 8f), A Egan (0-4).
Subs: N Ó Murchu for Stapleton 50, S Ryan for Healy 57.
Referee: A Mac Suibhne (Dublin).