The response of an optically injected quantum-dot semiconductor laser (SL) is studied both experimentally and theoretically. In particular, the nature of the locking boundaries is investigated, revealing features more commonly associated with Class A lasers rather than conventional Class B SLs. Experimentally, two features stand out; the first is an absence of instabilities resulting from relaxation oscillations, and the second is the observation of a region of bistability between two locked solutions. Using rate equations appropriate for quantum-dot lasers, we analytically determine the stability diagram in terms of the injection rate and frequency detuning. Of particular interest are the Hopf and saddle-node locking boundaries that explain how the experimentally observed phenomena appear.