Short-term rainfall prediction remains a critical challenge, especially in regions like Western India that are frequently affected by intense monsoons. This study proposes a hybrid deep learning framework that combines Convolutional Neural Networks (CNNs) for spatial feature extraction and Long Short-Term Memory (LSTM) networks for capturing temporal sequences. Trained on 20 years of hourly meteorological data from five cities in Maharashtra, India, the model utilizes 21 key weather attributes, including temperature, humidity, wind speed, and atmospheric pressure. To avoid data leakage and mimic operational conditions, a walk-forward chronological split was employed during evaluation. The model achieved a rainfall occurrence classification accuracy of 88% and a regression R2 score of 0.92, with RMSE and MAE of 0.20 and 0.18 respectively. SHAP (SHapley Additive exPlanations) analysis was employed to enhance interpretability, highlighting humidity and vapor pressure as dominant predictors. Compared to traditional machine learning baselines (Naïve Bayes, K-NN, Random Forest, Logistic Regression, and XGBoost) and standalone DL models (CNN and LSTM), the proposed hybrid showed superior predictive performance across all metrics. Furthermore, paired t-tests validated the statistical significance of improvements. This work delivers a transparent, statistically robust, and regionally grounded approach to rainfall prediction, aligning well with climate-resilient decision support systems. Future improvements include the incorporation of transformer-based architectures, domain adaptation for new geographic regions, and integration with real-time IoT-enabled weather stations for live forecasting and adaptive learning.