Striker Joe Mason started up front for City today in place of the exiting Kenwyne Jones and scored the winning goal.
Mason finished from close range in the 58th minute after Craig Noone's effort was blocked.
After a disappointing Christmas so far it was good to grind out a victory, a victory that closes the gap on the play off places to just four points.
Cardiff are now 9th in the table as they head into an 11 day break from League football.
Next weekend City entertain Shrewsbury in the FA Cup before an tough looking away fixture at Hull City on Wednesday week.