Soon after the hosts came within a whisker of a spectacular opener when Peter Whittingham's 30-yard free kick flew past the upright.
The number seven's left boot was Cardiff's most dangerous threat in the early stages and he tested Hart with a low drive after a quarter of an hour that was too central to really trouble the England number one.
City were controlling possession but didn't manage a shot on target until the 35th minute when David Silva was given space 20 yards out and curled a shot into the palms of David Marshall.
Moments later the visitors came close again when Jesus Navas's pullback was layed off by Edin Dzeko for Yaya Toure, whose snap-shot was well blocked by Ben Turner.
Campbell had two late chances to open the scoring but couldn't take either as first he was put off by Lescott's outstretched boot before failing to beat Hart from a tight angle.