Driver drowsiness significantly impacts global road safety, leading to numerous traffic accidents. While electroencephalogram (EEG) stands out for its direct assessment of cognitive states in drivers, the inherent variability of EEG signals poses substantial challenges to accurate decoding for driver state classification. To tackle this, we introduce a novel BCI framework for EEG-based driver drowsiness classification using test-time adaptation. To dynamically adjust to target distributions within online BCI framework, we utilizes a memory technique and optimizes batch normalization layers. We also introduce prototype learning for reliable predictions within distribution shift environments. Extensive experiments demonstrate that our framework effectively adapts to non-stationary EEG signals and varying subject states. Through our calibration-free framework, we address the critical challenge of online BCI framework for EEG-based driver drowsiness classification.