Drogheda United ... 1 Derry City ... 3Derry City put their miserable league form behind them to clinch a place in the last 16 of the FAI Cup.
Ciaran Martyn's goal soon after the interval proved crucial in a second-round tie which ebbed and flowed.
The visitors got off to the best start possible when they opened the scoring courtesy of Liam Coyle's penalty-kick in the 13th minute. Paddy McLaughlin doubled the lead 12 minutes later with a low shot from 25 yards.
Drogheda fought back and were rewarded on 33 minutes when Mark Dempsey, who has been plagued by injury since his arrival at the club during the close season, beat Gough with an angled shot.
But Derry sealed victory when Martyn forced the ball in from close range after Jamie Hughes's knock-back from Hutton's centre.
DROGHEDA: Rogers; Dunne, Gollogley, Lynch, Kelly; Gallagher, Taylor, Tierney, Dempsey; Quinless, O'Brien. Substitutes: Cronin for Tierney (76 minutes).
DERRY: Gough; McLaughlin, Kelly, McCallion, Hargan; Hutton, Doherty, Martyn, McCready; Beckett, Coyle. Substitutes: Friars for Beckett (45 minutes), Hughes for Coyle (49 minutes).
Referee: Pat Whelan (Dublin).