We propose a novel few-shot action recognition framework, STRM, which enhances class-specific feature discriminability while simultaneously learning higher-order temporal representations. The focus of our approach is a novel spatio-temporal enrichment module that aggregates spatial and temporal contexts with dedicated local patch-level and global frame-level feature enrichment sub-modules. Local patch-level enrichment captures the appearance-based characteristics of actions. On the other hand, global frame-level enrichment explicitly encodes the broad temporal context, thereby capturing the relevant object features over time. The resulting spatio-temporally enriched representations are then utilized to learn the relational matching between query and support action sub-sequences. We further introduce a query-class similarity classifier on the patch-level enriched features to enhance class-specific feature discriminability by reinforcing the feature learning at different stages in the proposed framework. Experiments are performed on four few-shot action recognition benchmarks: Kinetics, SSv2, HMDB51 and UCF101. Our extensive ablation study reveals the benefits of the proposed contributions. Furthermore, our approach sets a new state-of-the-art on all four benchmarks. On the challenging SSv2 benchmark, our approach achieves an absolute gain of 3.5% in classification accuracy, as compared to the best existing method in the literature.