Striker Craig Dove cut in from the right and a shot hard and low beyond Blues keeper Andy Marriott to give Boro a deserved 1-0 half time lead.
Blues were on the back-foot again early in the second half and two goal line clearances kept them in the game.
Boro's pressure finally told on 69 minutes however, and it was Dove again that doubled their advantage with a diving header inside the box from a left wing cross which left Marriott helpless.
Blues seemed to be woken up by this second goal and enjoyed a good spell - first Till was denied by an excellent save from Boro keeper Jones then Fagan had a good effort saved by the keeper.
Blues couldn't capitalise on this good spell of pressure however and came away from Teeside having suffered their first defeat in five games by the same scoreline as in the reverse fixture at Solihull.
Blues: Marriott, Cottrill, Capaldi, Carter, Hutchinson, Luckett, Till, Swierczewski, Kirovski (Barrowman 67), Fagan, Motteram (Allsop 53). Subs not used: Doyle, Hipkiss, Parratt.
Boro: Jones, Parnaby, Murphy, Smith, Davies (Captain), Vidmar, Johnston, Wilson, Cade (Graham 46), Dove, Downing (Liddle 77) Subs not used: Nordgren, Peacock, Russell.
Reserves Results 2002/03
