The one-cap England striker, who joined from Sunderland in January, netted either side of half-time to pile the misery on the Molineux club, for whom Bakary Sako reduced the deficit.
And while a ninth consecutive away match without defeat keeps the Bluebirds top - a position they have occupied since late November - an 11th game without a win means Wolves are facing the bleak prospect of a second consecutive relegation.
Gunnarsson's long throw was flicked into the path of Campbell and his header from six yards gave Ikeme no chance.
Within a couple of minutes of the restart, City had the ball in the net but Bellamy's effort from Ikeme's fumble was ruled out for offside.
There was no linesman's intervention when Campbell headed in Bellamy's cross after 67 minutes.