After Paul Furlong had missed a penalty for Blues, striker Craig Fagan opened the scoring on 75 minutes, heading home a Curtis Woodhouse cross.
Recent signing Tom Williams made it 2-0 with a left foot shot five minutes later, his first goal in Blues colours.
Furlong then made up for his penalty miss by scoring the third goal with a close-range header to make the score 3-0.
Blues have now had seven wins, one draw and one loss (Preston) since boss Keith Bertschin took charge of the second string at St. Andrews and this three points moved the side up to eighth in the Avon Insurance Premier League table.
Team: Bennett, Gill, Vickers, Hutchinson, T Williams, Woodhouse, Hyde, Sonner, Eaden, Furlong, Fagan.
Subs: Capaldi, Luntala, Evans, Davies, Parker.