To find out the astrophysical processes responsible for gamma-ray burst (GRB), it is crucial to discover and understand the relations between their observational properties. This work was performed in the GRB rest frames using a sample of 62 long Swift GRBs with known redshifts. Following the earlier analysis of the correlation between afterglow luminosity (L*a) and break time (T*a), we extend it to correlations between the afterglow and the prompt emission GRB physical parameters. We find a tight physical scaling between the mentioned afterglow luminosity L*a and the prompt emission mean luminosity 〈L*p〉45≡Eiso/T*45. The distribution, with the Spearman correlation coefficient reaching 0.95 for the most accurately fitted subsample, scales approximately as L*a∝〈L*p〉0.745. We have also analysed correlations of L*a with several prompt emission parameters, including the isotropic energy Eiso and the peak energy in the νFν spectrum, Epeak. As a result, we obtain significant correlations also between these quantities, discovering that the highest correlated GRB subsample in the afterglow analysis leads also to the highest prompt–afterglow correlations. Such events can be considered to form a sample of standard GRBs for astrophysics and cosmology.