We use new Suzaku observations of PKS 0745−191 to measure the thermodynamic properties of its intracluster medium (ICM) out to and beyond r200 (reaching 1.25r200) with better accuracy than previously achieved, owing to a more accurate and better understood background model. We investigate and resolve the tensions between the previous Suzaku and ROSAT results for PKS 0745−191, which are found to be principally caused by incorrect background modelling in the previous Suzaku analysis. We investigate in depth the systematic errors affecting this observation, and present temperature, density, entropy and gas mass fraction profiles reaching out to and beyond the virial radius. We find that the entropy profile flattens in the outskirts as originally observed in the previous Suzaku analysis, but that the flattening starts at larger radius. The flattening of the entropy profile and our mass analysis suggest that outside ∼17 arcmin (∼1.9 Mpc) the ICM is out of hydrostatic equilibrium or the presence of significant non-thermal pressure support.