Two goals in two minutes towards the end of the mini-derby mean the Blues will now face Bolton Wanderers in the final with the date to be announced in the next few days.
United had England keeper Ben Foster to thank for ensuring the Reds went in level at half-time following a dominant first half display from City.
Foster made four excellent saves to keep out the Blues in the first period, but he was eventually beaten on 77 minutes when Robbie Mak rounded him and slid the ball home after being put through by a superb Alex Nimely pass.
Andrew Tutte sealed the victory two minutes later when he burst through from midfield to arrow a low drive past Foster to make it 2-0.City played out the last ten minutes or so with some impressive controlled football to deservedly take their place in this season’s MSC final.