The socioeconomic losses caused by extreme daytime drowsiness are enormous in these days. Hence, building a virtuous cycle system is necessary to improve work efficiency and safety by monitoring instantaneous drowsiness that can be used in any environment. In this paper, we propose a novel framework to detect extreme drowsiness using a short time segment (similar to 2 s) of EEG which well represents immediate activity changes depending on a person's arousal, drowsiness, and sleep state. To develop the framework, we use multitaper power spectral density (MPSD) for feature extraction along with extreme gradient boosting (XGBoost) as a machine learning classifier. In addition, we suggest a novel drowsiness labeling method by combining the advantages of the psychomotor vigilance task and the electrooculography technique. By experimental evaluation, we show that the adopted MPSD and XGB techniques outperform other techniques used in previous studies. Finally, we identify that spectral components (theta, alpha, and gamma) and channels (Fp1, Fp2, T3, T4, O1, and O2) play an important role in our drowsiness detection framework, which could be extended to mobile devices.