The Belfast side will be considered favourites to progress to the semi-finals, with Derry now facing a difficult trip to Shelbourne next Monday night while Linfield host Glentoran.
Early in the second half, Derry created two glorious chances, Mark Farren set Ciaran Martyn up but his low drive was easily saved by Mannus.
A poor clearance from Murphy broke to Beckett and while he got power into his shot, the magnificent Mannus got a hand to the effort to clear the danger.
Derry kept pressing and went agonisingly close to taking the lead in the 60th minute.
Martyn did well again to feed Farren and when the Donegal lad attempted to chip over Mannus' head, the ball crashed off the crossbar with the keeper back-peddling.
With both substitute strikers O'Flynn and McHugh now on the pitch for the final ten minutes it was clear that Stephen Kenny was going for all three points and he was almost rewarded in the 83rd minute.
A deep Farren cross from the right saw O'Flynn race forward but the Cork man failed to get the telling touch and a glorious chance was lost.
With five minutes of additional time ordered, Derry continued to pound the Linfield defence but failed to get that vital slice of luck when inside the danger area.