Abstract <p> The process of high-frequency fluorescence of a two-level open quantum system with permanent electric dipole moment interacting with a pulse of nonresonant monochromatic electromagnetic (laser) field is modeled and studied by methods of nonequilibrium quantum statistical mechanics. The system in question is represented by a one-electron two-level asymmetric polar semiconductor quantum dot characterized by the electric dipole moment operator with unequal diagonal matrix elements in its ground and excited quantum states, and interacting with dissipative environment. The dot is permanently excited by incoherent pumping and is driven by an amplitude modulated pulse, whose monochromatic carrier frequency is much lower than the optical transition frequency of the quantum dot. We derive an analytical expression for the time-dependent fluorescence power spectrum as a function of the amplitude, duration, initial phase, and carrier frequency of the rectangular monochromatic driving pulse, as well as of the pumping intensity and observation time. We show that the pulse itself does not add any discernable amount of energy to the fluorescence intensity but rather facilitates redistribution of the energy incoherently pumped into the system over a plurality of spectral peaks that arise under the influence of the pulse instead of the initial stationary single-peaked fluorescence spectrum observed before the arrival of the pulse and after its departure. </p>