Derry never looked like losing this match, but their travelling support were hardly comfortable in their seats, with the cushion of a second goal not being delivered until Gareth McGlynn's effort 15 minutes from time.
The result keeps them pushing in the right half of the table while Drogheda's recent run of form has stuttered, with this loss adding to last week's defeat against Bohemians.
Eamon Zayed put the upset of alleged racist abuse behind him as he started this one just as he had done against the Drogs at the Brandywell in May -- by plundering a goal.
His 15th of the season was the result of a fine touch from Stewart Greacen, the Libyan international fending off Philip Hand before slotting home.
McGlynn and James McClean both had decent opportunities to increase the first-half lead, but their efforts were found wanting.
Drogheda saw a 38th-minute free-kick dealt with easily, before Patrick McEleney almost bagged a cracker after he latched onto Zayed's punt up-field. His excellent chip over Stephen Trimble was just off course. McClean had a fine night on the left and nine minutes into the second half he saw a great effort whistle just past Trimble's post.
McGlynn bagged the insurance goal 15 minutes from time, after McClean picked him out with a precise cross. The midfielder's header gave Trimble no chance.
Zayed bagged the third with a perfect finish on the final whistle, and again McClean was the man to deliver the all-important cross.
Drogheda United -- Trimble; C O'Brien, McNally, Ekanem, Hand; M O'Brien (Clarke 81), McMahon, Gannon, Brennan (Quigley 81); Mulvenna (Freeman 81); Corcoran.
Derry City -- Doherty; McCallion, McBride, Greacen, Lafferty; McGlynn, Higgins, S McEleney, McClean; Zayed, P McEleney (McLaughlin 90).
Ref -- D Tomney (Dublin)