Cameron Dummigan opened the scoring after six minutes with a stunning strike before Adam Foley equalised for the visitors.
Will Patching converted a penalty after Mark Connolly was fouled in the box to restore their lead.
Daniel Kelly then scored his first goal for the Candystripes with Patrick Hoban netting a fourth and Ciaran Col adding a late fifth to seal the victory which keeps them two points behind leaders Shelbourne.
In their first game back after the mid-season break, Derry started brightly on home soil and went close early through Kelly, whose shot was saved by Andrew Wogan.
They edged in front soon after as Drogheda failed to clear a cross from Ben Doherty and when the ball fell to Dummigan on the edge of the box he rifled home into the top corner.
Patrick Hoban then had a shot tipped over by Wogan before Drogheda drew level against the run of play.
Foley stabbed home from close range after Evan Weir’s corner hit Doherty and fell into the midfielder’s path.
Derry re-established their lead just three minutes later from the penalty spot when Foley went from hero to zero, hauling down Mark Connolly in an off the ball incident in the box.
Patching stepped up and coolly converted, sending Wogan the wrong way for his sixth goal of the season.
Paul McMullan dragged a low shot wide before Brian Maher was called into action on the stroke of half-time to deny Ryan Brennan.
It was a slow start to the second half from Ruaidhri Higgins’ side and Drogheda almost capitalised five minutes after the restart.
Jack Kearney’s low strike deflected past Maher, but the goal was disallowed for offside.
That seemed to jolt Derry into life, and they extended their lead on 57 minutes with Kelly racing onto a long ball before finishing well.
Things went from bad to worse for struggling Drogheda as Frantz Pierrot was sent off for a second yellow card just after the hour mark.
Moments later Hoban added a fourth goal after Kelly had headed Doherty’s cross into his path.
It was the prolific striker’s 12th goal of the season and he soon made way for the returning Colm Whelan, making his first appearance for Derry in over a year after an ACL injury.
It was fellow substitute Ciaran Col who would round off the scoring, heading home with his first touch since coming on to seal Derry’s biggest win of the season.
After four wins on the bounce, Derry will be hoping to make five in a row when they travel on Thursday night to take on seventh placed Sligo Rovers at the Showgrounds.
Derry City: Brian Maher, Cameron Dummigan (Ronan Boyce 85), Mark Connolly, Shane McEleney (Sam Todd 85), Ben Doherty (Ciaran Coll 85); Sadou Diallo, Adam O’Reilly, Will Patching (Colm Whelan 76); Paul McMullan, Pat Hoban (Daniel Mullen 70), Daniel Kelly.
Drogheda United: Andrew Wogan, Evan Weir (Evan Haddock 86), Andrew Quinn, Jack Keaney, Franta Pierrot, Adam Foley (Emre Topcu 75), Matthew O’Brien, Ryan Brennan (James Byrne 70), Luke Heeney, Conor Kane, Warren Davis.
Referee: Robert Harvey (Dublin).
Tags: