Goals from captain Ian Bermingham and Kurtis Byrne, on target for the third successive match, earned St Patrick's a first win in six games.
Such is the congestion at the foot of the table, the much needed victory for Liam Buckley's side lifts them off the bottom and out of the relegation zone up to eighth place.
With much welcome rain adding zip to the surface, St Pat's starting positively as Christy Fagan shot wide on five minutes after Kurtis Byrne cut back a deep cross from Darragh Markey.
And the Inchicore side were deservedly ahead from a training ground free kick routine two minutes later.
Conan Byrne's delivery from the right found the run of left-back Ian Bermingham, ghosting in on the far side. The skipper planted his low left foot shot past keeper Stephen McGuinness into the bottom corner of the net for a well-taken first goal of the season.
Maintaining their high tempo, St Pat's created a further chance on 12 minutes. Fagan got free down the left to cross with Conan Byrne shooting narrowly wide at the back post.
Minutes later McGuinness had to rescue Drogheda with a fine instinctive parry save as Markey let fly from inside the box.
And the oneway traffic just continued. Fagan was off target after a scramble from a corner before McGuinness got down well to save a drive from Kurtis Byrne.
The out-of-sorts Fagan shot wide again on 26 minutes after Conan Byrne spun Ciaran McGuigan to cross as Drogheda just couldn't get a foothold in the game.
Pete Mahon's side finally relieved the pressure on the half hour with Jake Hyland just not getting enough purchase on his header from Gareth McCaffrey's cross as Conor O'Malley gathered.
McGuinness then had to be there again at the other end with the stop of the half right on the break. Picked out by the impressive Markey's diagonal ball, Kurtis Byrne cut inside a defender only to see his shot pushed over the top by the busy visiting keeper.
The Drogheda keeper was beaten for a second time, though, two minutes after the interval.
Delightful skill by 19-year-old Markey on the left saw him beat a man before threading a sublime ball through for Kurtis Byrne who swept home off his right foot for an outstanding goal.
Drogheda continued to struggle to get into the game. McCaffrey was booked for dissent after not being awarded a penalty on 58 minutes after he'd gone to ground under O'Malley's challenge just inside the box.
Visiting skipper Luke Gallagher saw a speculative shot from distance go wide late on as St Patrick's eased to a comfortable win.