Driver drowsiness is one of the leading causes of road accidents worldwide, particularly in resource-constrained and high-variability environments where real-time monitoring is critical. To address this challenge, we present DRISTI (Driver Real-time Intelligent Spatio-Temporal Inference), a novel deep learning framework designed for efficient and accurate drowsiness detection. Unlike traditional convolution-based systems, DRISTI leverages a Vision Transformer (ViT) encoder to extract global spatial representations from facial frames, enabling the capture of fine-grained cues such as eye closure, yawning, and gaze shifts with reduced computational cost. These embeddings are modelled through a Long Short-Term Memory (LSTM) network to learn temporal behavioural dynamics, while an additive attention mechanism highlights the most informative segments, ensuring reliable recognition of both transient and sustained drowsiness. A dynamic frame selection strategy further reduces redundancy by retaining only behaviourally distinct frames, improving efficiency without compromising accuracy. DRISTI attains 89.9% Accuracy, 91.2% Macro F1, and 93.5% Weighted F1, with ROC-AUCs of 0.98 (Not Drowsy), 0.96 (Drowsy), and 0.92 (Transient Drowsy). These results indicate robust, class-balanced performance suited for safety-critical early-warning applications.