Caceres - making his second appearance for the Reserves - and Matthews should have added to the lead with chances before half time.
Carlisle pulled one back two minutes after the restart as Wake fired home from Harrison's cross, but City held on to their first half lead to come away 2-1 winners.
City line-up: Glennon; Morley, Mohan (Burton), Bloomer, Van Blerk (Price); Williams (Peat), Boyle, Matthews, Beresford; Dudfield, Caceres.
Un-used subs: Dixon, Bowsley.