A search for dark matter particles is performed using events with a pair of W bosons and large missing transverse momentum. Candidate events are selected by requiring one or two leptons (ℓ = electrons or muons). The analysis is based on proton-proton collision data collected at a center-of-mass energy of 13 TeV by the CMS experiment at the LHC and corresponding to an integrated luminosity of 138 fb⁻¹. No significant excess over the expected standard model background is observed in the ℓνqq and 2ℓ2ν final states of the W⁺W⁻ boson pair. Limits are set on dark matter production in the context of a simplified dark Higgs model, with a dark Higgs boson mass above the W⁺W⁻ mass threshold. The dark matter phase space is probed in the mass range 100–300 GeV, extending the scope of previous searches. Current exclusion limits are improved in the range of dark Higgs masses from 160 to 250 GeV, for a dark matter mass of 200 GeV.