We present clustering analyses of identically-selected star-forming galaxies in 3 narrow redshift slices (at z=0.8, z=1.47 and z=2.23), from HiZELS, a deep, near-infrared narrow-band survey. The HiZELS samples span the peak in the cosmic star-formation rate density, identifying typical star-forming galaxies at each epoch. Narrow-band samples have well-defined redshift distributions and are therefore ideal for clustering analyses. We quantify the clustering of the three samples, and of H-alpha luminosity-selected subsamples, initially using simple power law fits to the two-point correlation function. We extend this work to link the evolution of star-forming galaxies and their host dark matter halos over cosmic time using sophisticated dark matter halo models. We find that the clustering strength, r0, and the bias of galaxy populations relative to the clustering of dark matter increase linearly with H-alpha luminosity (and, by implication, star-formation rate) at all three redshifts, as do the host dark matter halo masses of the HiZELS galaxies. The typical galaxies in our samples are star-forming centrals, residing in halos of mass M_halo ~ a few times 10^12M_solar. We find a remarkably tight redshift-independent relation between the H-alpha luminosity scaled by the characteristic luminosity, L(H-alpha)/L(H-alpha)*(z), and the minimum host dark matter halo mass of central galaxies. This reveals that the dark matter halo environment is a strong driver of galaxy star-formation rate and therefore of the evolution of the star-formation rate density in the Universe.