Anthony Murphy's 25th minute strike proved the difference at United Park as Alan Matthews charges proved to be a sterner test than many may have expected.
Drogheda have now played 360 minutes of goaless football this season, and although they appear to have mastered the art of defence, they are still lacking in attack.
From their free flowing display last week against Shamrock Rovers, Bohemians looked a different side. They failed to string passes together and their distribution lacked potency as they played the ball across the field and most direct passes were overhit.
The central pairing of Alan McNally and Ian Ryan worked well considering their lack of playing time together, however other areas of the Drogheda team are still very much a work in progress. Former Bohs player John Paul Kelly and Robbie Martin spurned a good chance early on due to poor communication.
Murphy's goal came somewhat against the run of play. From the outset the home team made their intentions known as they closed down their opponents giving them no time on the ball.
Alan McNally lead the charge with a big tackle on Joseph Ndo right from the off as Bohs were put on the back foot straight away.
Brian Murphy, rated one of the best 'keepers in the league, had something of a Fabien Barthez moment as he tried to control a throw with his feet and almost lobbed himself as he flicked the ball over his head and nearly into the empty night after two minutes.
The Bohs shot stopper made a series of howlers, directing his clearances to Drogheda players who failed to capitalise on the chances.
Ndo showed flashes of brilliance and the prolific midfielder found himself against the entire Drogheda defence as Bohs quick counter attack found him in acres of space. But for the coverage of Ian Ryan NDo would have been clean through, but he was forced out to the side from where his cross failed to connect with any strikers.
Fenlon's half time speech didn’t seem to motivate his side much as it was the home side who came out of the blocks, sticking with their tactics of trying to stop Bohs playing.
Robbie Farrell, a second half sub, put the increasingly dubious looking Bohs defence under pressure and it paid off as he disposed Shelley but he snatched at his shot and Murphy seemed relieved to find the ball floating toward him. This was also Drogheda's first shot on target.
Fenlon introduced Drogheda native Killian Brennan to the game as Bohs looked to grab a second to kill off the game. Immediately he got stuck in, proving instrumental in several attacks that ultimately proved fruitless. But it was the visitng side who made the trip back down the M1with all three points as once again Drogheda are left to ponder what if.
Drogheda United: Steve Williams; Gavin Whelan, Ian Ryan, Aalan McNally, Robbie Clarke; Mark Duggan, John Paul Kelly, Paul Shiels (James Chambers 62), Paul Crowley; Dave O’Connor (Brian King 76), Robbie Martin (Robbie Farrell 32).
Subs Not Used: Paul Skinner (gk), Jamie Duffy.
Bohemians: Brian Murphy; Owen Heary, Jason McGuinness, Ken Oman, Brian Shelley; Anto Murphy, Gary Deegan, Paul Keegan, Joseph Ndo; Glen Crowe, Jason Byrne (Killian Brennan 70).
Subs not used: Matt Gregg (gk), Glenn Cronin, Sean Byrne, Conor Powell.
Referee: Dave McKeon
Attendance: 1,500 (estimate)