In this paper, we present asymmetric pivot manipulation for picking up rigid hollow objects to achieve a hole grasp. The pivot motion, executed by a position-controlled robotic arm, enables the gripper to effectively grasp hollow objects placed horizontally such that one gripper finger is positioned inside the object's hole, while the other contacts its outer surface along the length. Hole grasp is widely employed by humans to manipulate hollow objects, facilitating precise placement and enabling efficient subsequent operations, such as tightly packing objects into trays or accurately inserting them into narrow machine slots in manufacturing processes. Asymmetric pivoting for hole grasping is applicable to hollow objects of various sizes and hole shapes, including bottles, cups, and ducts. We investigate the variable parameters that satisfy the force balance conditions for successful grasping configurations. Our method can be implemented using a commercially available parallel-jaw gripper installed directly on a robot arm without modification. Experimental verification confirmed that hole grasp can be achieved using our proposed asymmetric pivot manipulation for various hollow objects, demonstrating a high success rate. Two use cases, namely aligning and feeding hollow cylindrical objects, were experimentally demonstrated on the testbed to clearly showcase the advantages of the hole grasp approach.