Glen Fitzpatrick sealed the points for Drogheda with a superb 74th minute strike against Dublin City at a wet and windy Dalymount Park.
Drogs could have had four or five but for a fine performance from City 'keeper Gary Rogers, an ex-Drogheda net minder.
The first shot on goal game on 12 minutes but Rogers went down bravely to deny Shane Barrett on the edge of the six yard box.
Rogers was back in action again on 16 minutes when he blocked a Declan O'Brien effort from close range.
Drogheda appealed for a penalty on 37 minutes when Shane Robinson went down in the box but referee Hugo Whoriskey waved their pleas away.
There was a great opening to the second half when Rogers made two saves in quick succession. Firstly he parried a Derek Tyrell shot from the left. The loose ball found O'Brien who struck a low shot but Rogers went down well again to make the save.
Drogs' Shane Barrett then broke loose on the right wing but Stuart Malcolm cleanly dispossessed him on the right of the area. City’s David Freeman got behind the Drogs defence on 62 and was one on one with ‘keeper Dan Connor but was ruled offside.
Drogheda always looked more likely to score and the opener came on 74 minutes.
Paul Keegan played James Keddy through on the left wing and Keddy squared to Glen Fitzpatrick who blasted past Rogers from 18 yards.
