Just as it looked as though the two sides would be heading into the break level, hosting Cardiff took a 42nd-minute lead. Peter Whittingham crossed for Joe Mason, who slotted the ball beyond the reach of Andy Lonergan from close range.
Leeds provided a greater attacking threat after the restart and went close to drawing level in the 62nd minute. However, Danny Pugh's strike from distance just went wide of the target.
Filip Kiss had Cardiff's best chance to regain the lead, but his effort from eight yards out went wide of goal.
Cardiff will be guaranteed a spot in the top six if Middlesbrough lose to Southampton this evening.