Higgs boson production cross-sections in proton-proton collisions are measured in the H→WW∗→eνμν decay channel. The proton-proton collision data were produced at the Large Hadron Collider at a centre-of-mass energy of 13 TeV and recorded by the ATLAS detector in 2015 and 2016, corresponding to an integrated luminosity of 36.1 fb−1. The product of the H→WW∗ branching fraction times the gluon-gluon fusion and vector-boson fusion cross-sections are measured to be 11.4+1.2−1.1(stat.)+1.8−1.7(syst.) pb and 0.50+0.24−0.22(stat.)±0.17(syst.) pb, respectively, in agreement with the Standard Model predictions.