This research presents a novel approach to sleep stage classification using singlechannel EEG data and a Random Forest Classifier, integrating advanced feature extraction and SMOTE to address class imbalance. EEG data were preprocessed to extract power band features and time-domain characteristics, such as mean, variance, skewness, kurtosis, and entropy measures (Shannon entropy, permutation entropy, and sample entropy). The study leveraged data from the EEG Fpz-Cz channel to ensure high-quality signal processing, creating epochs and applying a Random Forest model to classify sleep stages into Wake, N1, N2, N3, and REM. SMOTE was used to resample the dataset, ensuring balanced training for the model. The results demonstrated strong performance, with a classification accuracy of 93.5% and a Cohen's Kappa score of 0.92, indicating near-perfect agreement between predicted and actual sleep stages. This study introduces a robust method that simplifies sleep stage analysis by focusing on a single EEG channel, demonstrating its potential for efficient clinical and personal sleep monitoring.