The home side went ahead on 22 minutes when Ryan Brennan lashed a left-footed effort past Doherty.
Brian Gannon had another goal-bound effort blocked by Patrick McEleney, before Doherty showed good hands to hold onto a Sean Brennan free-kick from 40 yards.
Tiarnan Mulvenna was then denied by a last-ditch Barry Molloy tackle, and the scorer’s brother Sean wasted another decent chance after being put clear by Paul Crowley.
Derry had decent claims for a penalty waved away when Simon Madden’s cross struck the hand of Gavin Brennan, but after that it was one-way traffic.
Derry’s Molloy got his marching orders in the 75th minute for a second bookable offence, and Drogheda pressed home their advantage on 89 when Gannon shot past Doherty.
DROGHEDA UNITED: Sava; Quigley, McNally, Prendergast, Grimes; Gannon, Crowley, R Brennan, G Brennan; S Brennan (Breen, 86), Mulvenna (O’Brien, 82).
DERRY CITY: Doherty; Madden, Greacen, McBride (S McEleney, 25), McCaffrey; P McEleney (Deery, 74), Higgins (Morrison, 74), Molloy, McLaughlin; Farren, Patterson.
Referee: G Kelly.