Point cloud-based object/place recognition remains a problem of interest in applications such as autonomous driving, scene reconstruction, and localization. Extracting a meaningful global descriptor from a query point cloud that can be matched with the descriptors of the database point clouds is a challenging problem. Furthermore, when the query point cloud is noisy or has been transformed (e.g., rotated), it adds to the complexity. To this end, we propose a novel methodology, named TopoRec, which utilizes Topological Data Analysis (TDA) for extracting local descriptors from a point cloud, thereby eliminating the need for resource-intensive GPU-based machine learning training. More specifically, we used the ATOL vectorization method to generate vectors for point clouds. To test the quality of the proposed TopoRec technique, we have implemented it on multiple real-world (e.g., Oxford RobotCar, NCLT) and realistic (e.g., ShapeNet) point cloud datasets for large-scale place and object recognition, respectively. Unlike existing learning-based approaches such as PointNetVLAD and PCAN, our method does not require extensive training, making it easily adaptable to new environments. Despite this, it consistently outperforms both state-of-the-art learning-based and handcrafted baselines (e.g., M2DP, ScanContext) on standard benchmark datasets, demonstrating superior accuracy and strong generalization.