To cause a desired result by means other than the obvious or rational method. Imagine you want a dog to wag it's tail. You should make the dog happy, and the tail will wag. If you can't or won't make the dog happy, you can get the tail to wag by "wagging the dog".
When the college saw that black students were failing Calculus at a disproportionately high rate to their enrollment, they decided to wag the dog by making the tests less difficult.