Many researchers have found that one of the major contributing factors of road accidents is driver drowsiness. Heart Rate Variability (HRV) is a non-invasive method to observe the influence of autonomic nervous system (ANS) of the human body. The ANS consists of parasympathetic and sympathetic nervous activities and its relation to driver drowsiness is observed by means of HRV analysis. In this study, twenty-two subjects participated in an experiment based on simulated driving environment. The temporal changes for low frequency (LF), high frequency (HF) and LF/HF ratio are observed. LF and HF spectral powers show significant changes from alert to drowsy state. Paired t-test is used to find the statistical significance. The analysis shows that there is a significant (p<0.01) decrease in the LF/HF ratio when subject is in drowsy state. The observations also conclude with significance that LF decreases (p<0.001) and HF increases (p<0.05) from alert to drowsy state. This study shows very encouraging results that can be used to prevent drowsiness related accidents.