Drowsy driving significantly increases the risk of road accidents and crashes. However, the drowsy state remains difficult to detect in real-time. This study presents a supervised learning approach to driver drowsiness detection using heart rate variability (HRV) features derived from electrocardiogram (ECG) signals. The data was collected in a driving simulator from participants under different levels of sleep deprivation, with subjective sleepiness levels assessed with the Karolinska Sleepiness Scale (KSS). HRV features were extracted in both time and frequency domains composing a dataset. This dataset was used to train classification models, including neural networks and long short-term memory (LSTM) architectures. The experimental results show that HRV-based features can effectively model drowsiness levels, with LSTM models outperforming common baseline methods. Our approach copes with the progressive nature of the drowsiness state and contributes to the development of intelligent in-vehicle systems capable of non-invasively monitoring driver alertness and issuing timely alerts to prevent fatigue-related accidents.