The first evidence for off-shell Higgs production is reported in the final
state with two Z bosons decaying into either four charged leptons (muons or
electrons), or two charged leptons and two neutrinos, and a measurement of the
Higgs boson width is performed. Results are based on data from the CMS
experiment at the LHC at a center-of-mass energy of 13 TeV, corresponding to an
integrated luminosity of up to 140 fb$^{-1}$. The total rate of off-shell Higgs
boson production beyond the Z boson pair production threshold, relative to its
standard model expectation, is constrained to the interval [0.0061, 2.0] at 95%
confidence level. The scenario with no off-shell production is excluded at
99.97% confidence level (3.6 standard deviations). The width of the Higgs boson
is extracted as $Γ_{\mathrm{H}}$ = 3.2$_{-1.7}^{+2.4}$ MeV, in agreement
with the standard model expectation of 4.1 MeV. The data are also used to set
new constraints on anomalous Higgs boson couplings to W and Z boson pairs.