Higgs boson production via gluon-gluon fusion is measured in the WW *-> e nu mu nu decay channel. The dataset utilized corresponds to an integrated luminosity of 139 fb(-1) collected by the ATLAS detector from root s = 13TeV proton-proton collisions delivered by the Large Hadron Collider between 2015 and 2018. Differential cross sections are measured in a fiducial phase space restricted to the production of at most one additional jet. The results are consistent with Standard Model expectations, derived using different Monte Carlo generators.