© AP Photos
The hosts dominated the first half, but a series of solid saves from Tykes keeper Luke Steele ensured that there were no goals in the opening 45 minutes.
The visitors' first chance of the match came shortly after the re-start, as Bobby Hassell headed towards goal, but his effort was wide of the post.
However, the home side continued to look the more likely to score, eventually breaking the deadlock in the 59th minute, as Ben Turner fired the ball in from close range following a Kim corner.
The league leaders almost added a second two minutes later, when Bellamy crossed the ball in for Mutch, but the midfielder's shot was deflected wide.
Barnsley almost leveled moments later following a corner, but Leon Barnett headed off the line to keep the hosts ahead.
Cardiff switched to a more defensive style in the final minutes of the game, allowing Tomasz Cywka to test David Marshall with a powerful strike but the Scottish international was able to keep the shot out.
Barnsley continued to press for an equaliser, as Cywka took another shot deep into stoppage time with a deflection off Stephen Foster catching Marshall out, allowing the visitors to share the spoils.
The result leaves Cardiff six points clear at the top of the Championship table, while Barnsley climb to 19th.