Serb here, passionate about learning history so I will try to do my best.

First, Yugoslavia had a pact with Germany that allowed them to move troops whenever the wanted. But a few years before the war started there was a coup (British influenced and staged) in Belgrade which put to power the government which declared the pact non-standing and that pretty much angered Hitler. At this point Yugoslavia was starting to bother him.

Second, in order the break up Yugoslavia, he had to support the Croats because Serbs were the cohesion factor (which didn't make other nations happy but that is another subject). Croats were trying to get independence from 1925 - in one shape or another and serbian monarch and Belgrade government always found a way to stop it from happening. So Croats welcomed the idea of breaking up Kingdom of Yugoslavia.

Third the Serb - Croat feud was reaching a climax (you can see all the horrible things Croats did to Serbs in WWII, especially the only children concentration camp in WWII - Дечји логор у Сиску) and Hitler just picked a side which favored his interests and pushed the button..

Sry for bad english and am open to questions.