Brett Hinks opened the scoring for Blues on 32 minutes and Boro looked to have snatched a point when Tom Craddock equalised wih just five minutes remaining.
Finland Under 21 international striker Njazi Kuqi bagged the winner for Keith Bertschins side with 4 minutes remaining.
Blues: Vaesen, Cottrill, Alsop, Oji, Painter, Hinks, Wright, Howland, Till, Kuqi, Birley. Subs: Dormand, Parratt, James Blake, Curtis, Hamilton.
Boro: Knight, Johnson, Radcliffe, Grounds, Davies, Johnson, Robson, Kennedy, Peacock, Lemaire, Craddock. Subs: Pennock, Reveley, Bainbridge, Fisher.