Multi-object tracking (MOT) in monocular videos is fundamentally challenged by occlusions and depth ambiguity, issues that conventional tracking-by-detection (TBD) methods struggle to resolve owing to a lack of geometric awareness. To address these limitations, we introduce GRASPTrack, a novel depth-aware MOT framework that integrates monocular depth estimation and instance segmentation into a standard TBD pipeline to generate high-fidelity 3D point clouds from 2D detections, thereby enabling explicit 3D geometric reasoning. These 3D point clouds are then voxelized to enable a precise and robust Voxel-Based 3D Intersection-over-Union (IoU) for spatial association. To further enhance tracking robustness, our approach incorporates Depth-aware Adaptive Noise Compensation, which dynamically adjusts the Kalman filter process noise based on occlusion severity for more reliable state estimation. Additionally, we propose a Depth-enhanced Observation-Centric Momentum, which extends the motion direction consistency from the image plane into 3D space to improve motion-based association cues, particularly for objects with complex trajectories. Extensive experiments on the MOT17, MOT20, and DanceTrack benchmarks demonstrate that our method achieves competitive performance, significantly improving tracking robustness in complex scenes with frequent occlusions and intricate motion patterns.