The Sky Blues raced into a two-goal lead inside the first quarter of an hour at Damson Park with goals from Andy Whing and Colin Cameron.
Mikael Forssell reduced the deficit to 1-2 from the penalty spot on 25 minutes but Coventry restored their two-goal advantage within a minute through Matt West.
West scored his second of the night and the Sky Blues fourth just past the hour mark.
DJ Campbell then bagged a brace for Blues to make the score 3-4 and despite a late rally from Keith Bertschin's side the vistors held on to book their place in the final where they will meet either Redditch Utd or Walsall.
Coventry: Lee-Barrett, Whing, Giddings, Cameron (Jones 65), Page, Bunce, McNamee (Hildreth 33), Gooding, West, Fadiga(Burtoft 46), Lynch. Subs not used: Belford,Duggan
Blues: Legzdins, Howland, Campion, Pearce, Price, Danns (Dicker 61), Wright, Kilkenny, Forssell (McPike 61), Campbell. Birley. Subs not used: Lyness, Kavanagh, Hall.