A fractional-rotation latching system with retrofit capability which includes, in its most preferred embodiment with reference to an example vending machine environment, a T-handle housing to be connected to a vending machine door, a T-handle designed to be nested at least partially within the T-handle housing, a key-operated cylinder lock contained within the T-handle and including a radial lock bolt, a fractional-rotation post member connected to the T-handle, corresponding receiving assembly connected to the vending machine frame for receiving the post member, thereby creating a link sufficient to secure the vending machine door to the vending machine frame, a rotation limitation assembly connected to the post member which includes a cam washer and a flanged washer located within the T-handle housing, and a guide block interposed between the post member and the T-handle to secure a continuously engaging connection between the post member and the T-handle and to limit axial movement between the T-handle and the T-handle housing to an arrangement where the lock bolt is readily externally accessible.