The Boynesiders looked to be heading for a semi-final clash against neighbours Dundalk when Derek Prendergast struck after 79 minutes, but a fortuitous last-gasp Vinny Faherty goal forced extra time.
Pats keeper Barry Murphy then saved spot kicks from Drogheda’s Tiarnan Mulvenna and Brennan brothers Ryan and Gavin, while Sean O’Connor, Jake Kelly and Faherty netted their penalties for Pats.
Drogheda were quickly into their stride in normal time and created the game’s first chance when a fine passing move ended with a Ryan Brennan shot that flew just wide.
The Inchicore took charge and Sean O’Connor’s vicious 25-yard drive flew narrowly wide before a Chris Forrester shot was parried by keeper Gabriel Sava and out for a corner via the chest of Brian Gannon on the goalline.
There was controversy on the half-hour mark when Ryan Brennan’s cross picked out brother Gavin who headed past Barry Murphy, only to have the goal ruled out for a push by the Drogheda winger.
There was more bad luck for the Boynesiders’ talisman two minutes later when his downward header from a Philip Hand corner bounced up off the turf and onto the crossbar.
After half-time Bolger just failed to get a header on target from an Ian Bermingham centre, but then it was Drogheda who nearly struck, John Sullivan’s shot from 18 yards blocked by Jake Carroll.
Drogheda carved out a great chance for the lead goal on 74 minutes when Gavin Brennan’s near-post cross looked tailor-made for Declan O’Brien, but somehow he failed to get a touch.
The Boynesiders finally broke the deadlock with 11 minutes left. Hand’s deep corner was met by Derek Prendergast who beat Murphy with a close-range header.
They couldn’t hang on until full-time, however, as a free kick was whipped into the box in the 90th minute and the ball ricocheted off Faherty and into the net to force extra time.
The chances dried up in extra time as both sides tired and so it was onto penalties, with Pat’s coming through to earn a semi-final tie against Dundalk at Oriel Park as the draw for the last four was made last night. Derry City will play Shels in the other semi-final.
DROGHEDA UNITED: Sava; Gannon, McNally, Prendergast, Hand; O’Brien, R Brennan, Foley, Sullivan, G Brennan; Hynes.
Subs: Quigley for Sullivan (85min), Mulvenna for O’Brien (105min), S Brennan for R Brennan (106min).
ST PATRICK’S ATHLETIC: Murphy; O’Brien, Flynn, Kenna, Bermingham; Chambers, Carroll, Bolger, Forrester; Faherty, O’Connor.
Subs: J Kelly for Forrester (67min), Price for O’Brien (73min), O’Flynn for Bolger (82min).
Referee: D Hancock (Dublin).