Goals from Gavin Brennan and Ryan Brennan saw Mick Cooke's side take a well-deserved three points from the Brandywell
After an early moment of panic in the Drogheda box which goalkeeper Michael Schlingermann had to clear, the game's pace slowed considerably, with neither side really getting a foothold on the match. Cathal Brady was lively for the visitors, and provided a decent cross for Gavin Brennan, but the midfielder headed just over.
Derry's best chances of the half fell to Michael Duffy and Ruaidhri Higgins, but neither player could direct their efforts on target. With half-time approaching, Drogheda took a surprising lead as Gavin Brennan headed in after Ger Doherty saved Declan O'Brien's initial effort.
Ryan Brennan doubled Drogs' lead from the spot seven minutes into the second-half after a foul by Shane McEleney, while Patrick McEleney went close with a low effort at the other end of the pitch. A double substitution spurred on the hosts, but they could not really test Schlingermann with the defence standing firm.
Rory Patterson had a few half-chances as the game wound down, but Derry never really looked like getting back into the game, leaving them eight points behind league leaders St Patrick's Athletic.