Measurements of the fiducial inclusive and differential production cross sections of the Higgs boson in proton-proton collisions at √s = 13 TeV are performed using events where the Higgs boson decays into a pair of W bosons that subsequently decay into a final state with an electron, a muon, and a pair of neutrinos. The analysis is based on data collected with the CMS detector at the LHC during 2016-2018, corresponding to an integrated luminosity of 137 fb^-1. Production cross sections are measured as a function of the transverse momentum of the Higgs boson and the associated jet multiplicity. The Higgs boson signal is extracted and simultaneously unfolded to correct for selection efficiency and resolution effects using maximum-likelihood fits to the observed distributions in data. The integrated fiducial cross section is measured to be 86.5 ± 9.5 fb, consistent with the Standard Model expectation of 82.5 ± 4.2 fb. No significant deviation from the Standard Model expectations is observed in the differential measurements.