Recently, the relation between the masses of the black hole (M_BH) and the host galaxy (M_host) in quasars has been probed down to the parameter space of M_BH ∼ 10⁸ M_⊙ and M_host ∼ 10¹¹ M_⊙ at z < 0.5. In this study, we have investigated the M_BH–M_host log-linear relation for a sample of 37 quasars with low black hole masses (10⁷ M_⊙ < M_BH < 10^8.3 M_⊙) at 0.5 < z < 1.0. The black hole masses were derived using virial mass estimates from Sloan Digital Sky Survey (SDSS) optical spectra. For 25 quasars, we detected the presence of the host galaxy from deep near-infrared H-band imaging, whereas upper limits for the host galaxy luminosity (mass) were estimated for the 12 unresolved quasars. We combined our previous studies with the results from this work to create a sample of 89 quasars at z < 1.0 having a large range of black hole masses (10⁷ M_⊙ < M_BH < 10¹⁰ M_⊙) and host galaxy masses (10¹⁰ M_⊙ < M_host < 10¹³ M_⊙). Most of the quasars at the low-mass end lie below the extrapolation of the local relation. This apparent break in the linearity of the entire sample is due to increasing fraction of disc-dominated host galaxies in the low-mass quasars. After correcting for the disc component, and considering only the bulge component, the bilinear regression for the entire quasar sample holds over 3.5 dex in both the black hole mass and the bulge mass, and is in very good agreement with the local relation. We advocate secular evolution of discs of galaxies being responsible for the relatively strong disc domination.