Drogheda made a confident start and nearly exposed some sloppy defensive play in the eighth minute when Dinny Corcoran got in behind Dave Mulcahy and hooked a low shot into the side netting from a tight angle.
Pat’s striker Daniel North had his first sight of goal on 11 minutes when he was put through by strike partner Ian Daly, but could only shoot weakly into the arms of keeper Stephen Trimble.
An untidy spell of play followed as the final ball went awry at both ends, before Dave Mulcahy headed over the bar from a Stephen Bradley corner for the visitors.
Pat’s created another opportunity on 34 minutes when Ian Bermingham played a great one-two with Stephen Bradley before driving into the box and firing across the face of goal.
That signalled a strong finish to the first half from the visitors, with Daly hooking a shot over the bar before North — easily the Inchicore side’s most dangerous player — nodded against the outside of the post after a half-cleared corner had been sent back in towards the far post.
The game exploded into life with two goals in 60 seconds at the start of the second period. First, Bermingham burst down the left flank and crossed for Daryl Kavanagh to side-foot Pat’s into a deserved lead.
Then Drogs went straight up the field and got back on level terms. Philip Hand played a one-two with Tiarnan Mulvenna before teeing up Corcoran, who fired decisively past keeper Gary Rogers.
Drogs nearly got their noses in front from their next attack when Corcoran found himself in a similar position after being set up by David Freeman, but this time Rogers diverted his shot.
Evan McMillan headed narrowly over from a Bradley corner in response, but it was only after the introduction of Murphy that the visitors regained the lead.
After forcing a save from Trimble with his first touch, the substitute ghosted away from his marker to head home Bradley’s free kick on 71 minutes.
Three minutes later Murphy turned provider with a cross which was nodded back by North for Derek Doyle to head in.
Four minutes from time Daly tapped in goal number four for Pat’s after North had burst forward from his own half and unselfishly teed him up.
DROGHEDA UNITED: Trimble; Nolan (Hanaphy 80), McNally, Ekanem, Hand; M O’Brien, Gannon, Quigley, Freeman (McNamara 76); Mulvenna, Corcoran.
ST PATRICK’S ATHLETIC: Rogers; Hanley, E McMillan, Mulcahy (Murphy 68), Bermingham (Carroll 64); Kavanagh, Bradley, McFaul (Crowley 77), Doyle; Daly, North.
Referee: Paul Tuite (Dublin).