Visiting Cardiff dominated large parts of the half and eventually broke the deadlock with 20 minutes played.
The league leaders continued to push forward and went close to doubling their advantage when Campbell guided a cross from the left just wide of the target.
Wolves struggled to create many chances throughout, with their best falling to Bakary Sako inside the area in the 40th minute. However, the winger only succeeded in sending his scuffed shot off target.
Victory for the away side would see them open up an eight-point gap at the top of the table.