Kaminsky also had eight rebounds for the Badgers (3-0), who struggled late after coming off a 59-53 victory over No. 10 Florida.
He scored with 3:05 left, giving Wisconsin a 64-60 advantage, but the Badgers didn't get another field goal after that.
It took Josh Gasser's two free throws with 26 seconds left to nail down the triumph.
Sam Dekker contributed 13 points with seven rebounds, and Gasser finished with 11 points and six rebounds for Wisconsin.
Keifer Sykes provided 32 points but missed a potential tying 3-pointer at the buzzer for the Phoenix (1-1).