There was a very physical tone set early, which favored Duke's style of defense. They were letting a lot of contact go, especially on the guards, throughout the game. Most of the fouls in the early part of the game were pretty blatant, with some bizarre ticky tack ones thrown in for flavor.
If anything, I think Wisconsin was probably slightly ahead in the ref lottery at the half, but the style of play overall did not play well to their style.
Still, it was largely Okafor vs. Kaminsky, and Kaminsky was winning that fight. If the game continued in that vein, Wisconsin probably would have pulled it out. Duke was trying to run their offense through Okafor, who wasn't drawing double teams and wasn't making much hay against Kaminsky, either.
Then Okafor went out - and the game dynamic changed completely. Without Okafor in, Duke went completely away from feeding their bigs - because Okafor was their only post player who had a shot against Kaminsky. Instead, they turned to their guards - and their guards showed up big. Wisconsin's strength on defense is against big men, and it showed - Duke's guards were just faster and more talented than Wisconsin was able to handle, and that was allowing Duke to come back even with Okafor and Winslow on the bench.
And once it was tied late, the officials swung hard toward Duke. Winslow and Okafor should have both fouled out of the game. Winslow should have been gone before either of his out of bounds weren't called. Okafor should have been gone before the three point play. Kaminsky got yanked hard to the ground after a rebound. The refs were swallowing their whistle on some pretty big calls, and the physicality stepped up to a still higher level than it had been all game - and Wisconsin couldn't handle it.
The officiating impacted the outcome - but, it wasn't insurmountable. Wisconsin couldn't defend Duke's guards, they didn't adapt well to the more physical play the refs were allowing, they didn't handle Duke's zone very well when it appeared, and they didn't exploit their mismatches underneath when Okafor/Winslow were on the bench. Ryan got outcoached after Krzyzewski adapted to Okafor's foul trouble.