The Dragon’s side contained some nine professional players – including former City player Jeff Whitley – but were outplayed for large parts by the Blues’ young guns.
Abdi Ibrahim, who was outstanding on the night, scored the first goal on the stroke of half time with a diving header from Cunningham’s corner.
And two minutes after the break a fine Ben Morris down the wing saw him cut in and earn a penalty. Jack Redshaw stepped up to sent the keeper the wrong way and double the advantage.
Despite some Wrexham pressure in the second half, City stood firm and made it 3-0 on 87 minutes after good play by Ibrahim, he found James Poole who smashed it home to wrap up a hugely impressive performance.
City:
Clegg, Robinson, Morris, Paldan, Brown, Tsiaklis (Carter 71), Cieslwicz, Ibrahim, Redshaw (Hulme 61), Poole, Cunningham (Mancini 87).
unused subs: Varga, Johansen.
The two teams now meet again tomorrow at Hyde United in the same competition - kick-off is 7pm.