A tooling system has means for applying a vacuum to hold the fastener at the working end of the tool. A cavity in a hollow pusher pin has lateral ports for exclusively providing a airway between the vacuum source and the fastener. In other embodiments of the invention the pusher pin has fastener-gripping jaws in the form of balls moveable within lateral passageways in the pusher pin open into the cavity. The balls are biased inwardly against the fastener by an outer elastic band on the tool body which encircles the pusher pin. When adapted for installing magnetic-release type fasteners, the bottom end of the pusher pin is of reduced diameter for insertion into a magnetic release fastener. The fastener-receiving panel is supported by an anvil having a magnet whereby the fastener is released from the pusher pin as the fastener is pressed into the panel.