Blues new signing Robbie Savage made his Blues debut, playing for all of the first half, and he was the victim of some rash tackles from the Exeter midfielders.
Striker Andrew Johnson scored the only goal of the game 18 minutes into the second half.
Five minutes earlier midfielder Curtis Woodhouse had an effort ruled out for off-side.
Thirteen minutes from time Damien Johnson came close to doubling Blues lead and the game drew to a close with Blues well on top and never in danger of surrendering their advantage.
Exeter 0 - Blues 1
SQUAD: Vaesen, Bennett, Kenna, Eaden, Grainger, Williams, Tebily, Purse, Michael Johnson, Savage, Hughes, Devlin, Hyde, Woodhouse, Damien Johnson, Lazaridis, Andrew Johnson, Horsfield, John.