A piston pump includes a piston assembly which has a first piston element, a second piston element, and at least one transverse bore which corresponds to a longitudinal bore. The piston pump further includes a cylinder in which the piston assembly is guided in a longitudinally movable manner, and an inlet valve which includes a cage element, in which an inlet valve spring and sealing element are arranged, and a corresponding inlet valve seat which is arranged on the piston assembly. The inlet valve sealing element can be pressed sealingly into the corresponding inlet valve seat by means of a restoring spring in order to close off the longitudinal bore. The second piston element is configured as a sleeve made of a wear-resistant material, which accommodates axially acting power components. The inlet valve seat is disposed on a bending edge of the second piston element configured as a sleeve. The at least one transverse bore corresponding to the longitudinal bore is placed in the second piston element. The invention further relates to an associated braking system.