actually the Spanish didn't overthrow the Classical Maya. Their civilization mysteriously disappeared around 1100 AD. The Spanish overthrew the Aztec and Incan civilization. In my book 2012: The Return of Quetzalcoatl I explore the thesis that this had more to do with the new form of consciousness represented by the Spanish, rather than their superior armaments etc. This theory was developed by the philosopher Jean Gebser in his extraordinary work, The Ever-Present Origin.
We don't know why the Maya disappeared - it may be due to warfare or ecological overshoot as Jared Diamond proposes. However it may also be that for a people so precisely attuned to cycles of time, they did not expect their civilization to last forever - they were aware that they were codifying a system of knowledge (about time, synchronicity, resonance, etc) to leave for us to rediscover as we approach the end of the age. This is the interesting thesis developed by Jose Arguelles in The Mayan Factor.