We introduce a new method to detect solar-like oscillations in frequency power spectra of stellar observations, under conditions of very low signal-to-noise ratio. The Moving-Windowed-Power-Search (MWPS) searches the power spectrum for signatures of excess power, over and above slowly varying (in frequency) background contributions from stellar granulation and shot or instrumental noise. We adopt a false-alarm approach to ascertain whether flagged excess power, which is consistent with the excess expected from solar-like oscillations, is hard to explain by chance alone (and hence a candidate detection). We apply the method to solar photometry data, whose quality was systematically degraded to test the performance of the MWPS at low signal-to-noise ratios. We also compare the performance of the MWPS against the frequently applied power-spectrum-of-power-spectrum (PS⊗PS) detection method. The MWPS is found to outperform the PS⊗PS method.