Continuing where he left off at the Carlisle Grounds last week, Anto Flood made it two wins from two for Bohemians to put them top of table.
Flood rifled home the Gypsies’ third goal at Bray on the opening night and he finally put Drogheda to the sword before a healthy home crowd at Dalymount.
The only goal of the game came on 57 minutes, but was no more than Bohemians’ utter dominance deserved.
Mark Rossiter whipped over a super ball from the right and Flood scored with a superbly controlled first time side-foot shot past keeper David Quirke.
Bohemians should have doubled their winning margin on 82 minutes but for a shocking miss by Lee Dixon, who blazed Christy Fagan’s pass over the bar with only Quirke to beat.
Not unexpectedly, Bohemians dominated the first half with Drogheda thankful at the interval for a fine save from their young goalkeeper Quirke on 29 minutes the most noteworthy opening.
Fagan showed superb touch to control Killian Brennan’s ball into the area and spin past central defender Gareth Whelan. Quirke, a reserve at Monaghan last season, got out and down promptly to save the low drive with his feet.
Dixon had a goal bound shot blocked while Aidan Price headed narrowly wide from a Brennan corner as Bohemians trooped off frustrated to have no tangible reward for their first half effort.
Bohemians: Murphy; Rossiter, Heary, Price, Cahill; Dixon, O’Brien, Traynor (Somers, 82 mins.), Brennan; Flood, Fagan.
Drogheda United: Quirke; Gannon, McNally (Nolan, 66 mins.), Whelan, Hand; McNamara (C. O‘Brien, 70 mins.), McCrossan, M. O’Brien, Lester, Freeman; Corcoran.
Referee: Richie Winter (Dublin).