CPT violation has the potential to explain all three existing neutrino anomalies without enlarging the neutrino sector. CPT violation in the Dirac mass terms of the three neutrino flavors preserves Lorentz invariance, but generates independent masses for neutrinos and antineutrinos. This specific signature is strongly motivated by braneworld scenarios with extra dimensions, where neutrinos are the natural messengers for Standard Model physics of CPT violation in the bulk. A simple model of maximal CPT violation is sufficient to explain the existing neutrino data quite neatly, while making dramatic predictions for the upcoming KamLAND, Borexino and MiniBooNE experiments. Furthermore we obtain a promising new mechanism for baryogenesis.