Darragh Hanaphy drilled a low shot past Mervue keeper TJ Forde in the seventh minute after Dinny Corcoran’s header had been parried.
Mervue shook off that nervy start, however, and went on to dominate the second quarter, and James Casserley knocked the loose ball off the crossbar from a corner.
Mervue carried that momentum into the second half and Drogs had a huge let-off on 56 minutes when Trimble pushed King’s shot onto the post from point-blank range.
Drogheda’s patience was rewarded with three goals in six minutes. On 78 minutes Corcoran raced onto a McCrossan pass and rounded Forde before tapping into an empty net.
Then David Freeman struck twice in the space of 90 seconds, heading home a Colin O’Brien cross before lashing the ball to the Mervue net from just inside the box.
DROGHEDA UNITED: Trimble; C O’Brien, Gannon, Ekanem, Hand; M O’Brien, Quigley, McCrossan, McNamara; Hanaphy, Corcoran. Subs: Freeman for McNamara (60), Gaul for McCrossan (89), Murray for C O’Brien (89).
MERVUE UNITED: Forde; Crehan, Conneely, Casserley, Cunningham; King, Mountney, Varley, Molloy; Gaffney, Goldbey. Subs: Lee for King (78), Ludden for Casserley (82), Dravins for Goldbey (82).
Referee: Derek Tomney (Dublin).