Gliomas are the most prevalent type of primary brain tumors, and their accurate segmentation from MRI is critical for diagnosis, treatment planning, and longitudinal monitoring. However, the scarcity of high-quality annotated imaging data in Sub-Saharan Africa (SSA) poses a significant challenge for deploying advanced segmentation models in clinical workflows. This study introduces a robust and computationally efficient deep learning framework tailored for resource-constrained settings. We leveraged a 3D Attention UNet architecture augmented with residual blocks and enhanced through transfer learning from pre-trained weights on the BraTS 2021 dataset. Our model was evaluated on 95 MRI cases from the BraTS-Africa dataset, a benchmark for glioma segmentation in SSA MRI data. Despite the limited data quality and quantity, our approach achieved Dice scores of 0.76 for the Enhancing Tumor (ET), 0.80 for Necrotic and Non-Enhancing Tumor Core (NETC), and 0.85 for Surrounding Non-Functional Hemisphere (SNFH). These results demonstrate the generalizability of the proposed model and its potential to support clinical decision making in low-resource settings. The compact architecture, approximately 90 MB, and sub-minute per-volume inference time on consumer-grade hardware further underscore its practicality for deployment in SSA health systems. This work contributes toward closing the gap in equitable AI for global health by empowering underserved regions with high-performing and accessible medical imaging solutions.