Asa Hall went close to doubling the lead for Blues on 70 minutes but his powerful header was well saved by former Blues keeper Ryan Price.
Blues secured victory ten minutes from time with a superb solo effort from Wright. The young Blues winger finished off a mazy run down the left by cutting inside the Rushall defence to fire home from just outside the box.
Keith Bertschin's side will now meet the winners of the other semi-final between Redditch and Wolves in the final.
Blues: Meredith, James Blake, Alsop, Oji, Painter, Howland, Wright, Asa Hall, Barrowman, Till, Birley. Subs: Holtham, Price, Howell, Mark Hall, Davies.
Rushall Olympic: Price, Campbell, Dunn, Davies, Mitchell, Brown, Barnfield, Allen, Kitching, Porter, Truman. Subs: Holdcroft, O'Connor, Barnett, Walker, Shaw.