Derry moved one point off the top of the Premier Division after beating the leaders at the Brandywell.
City created the better chances in the first half with Ruaidhri Higgins and Eamon Zayed going close.
Daniel Lafferty fired in the only goal on 54 minutes from a 30-yard free-kick, but it required a blunder by keeper Alan Mannus for the ball to sneak in.
Rovers pressed for the equaliser but a series of superb saves from Gerard Doherty saw Derry hold on for the win.
A frantic first-half produced little in the way of good football and it took 24 minutes before the first serious attempt on goal.
Higgins ran on to a dropping ball but with Mannus stranded he headed over from 10 yards.
Zayed had a weak shot saved before Doherty blocked Gary Twigg's close-range strike with his legs.
A backpass was intercepted by Zayed on 39 minutes and he was left with just Mannus to beat but the former Linfield stopper made a good save to deny to the striker.
The opening 45 minutes ended with desperate defending from the Dubliners and Derry firmly on top.
Lafferty gave the hosts a derserved but fortunate lead with his free-kick, with the ball taking a bounce before slipping beyond the grasp of Mannus and into the net.
James McClean, who was being watched by Reading boss Brian McDermott and other cross-channel clubs, broke through before firing into the side-netting.
The leaders piled on the pressure in the last 15 minutes and Doherty pushed up a Dean Kelly volley before clawing the dropping ball off the goal-line.
Doherty's best save came with six minutes left, tipping Billy Dennehy's curling free-kick onto the crossbar.
The points were sealed when Doherty's reflex saved kept out Twigg's fierce shot in inury-time.