This paper reports on a distributed fiber sensing scheme to achieve sub-metric spatial resolution and long sensing ranges based on a differential pulse-width pair (DPP) Brillouin sensor. The scheme uses a scanning method in which the spectral separation between the two probe sidebands is kept constant, while the optical frequency of the pump is swept to scan the Brillouin spectral response. Experimental results show that the method avoids detrimental temporal distortions of the pulses, which in a standard implementation prevent the DPP method to operate over long distances. Here we demonstrate that this novel scanning method enables distributed sensing over 37.5 km with a spatial resolution of 20 cm and a frequency uncertainty of 1.9 MHz, obtained with 2k averages in a measurement time of a few minutes.