Abstract Differential cross-section measurements are presented for the electroweak production of two jets in association with a Z boson. These measurements are sensitive to the vector-boson fusion production mechanism and provide a fundamental test of the gauge structure of the Standard Model. The analysis is performed using proton–proton collision data collected by ATLAS at $$\sqrt{s}=13\ \hbox {TeV}$$ s = 13 TeV and with an integrated luminosity of $$139\ \hbox {fb}^{-1}$$ 139 fb - 1 . The differential cross-sections are measured in the $$Z\rightarrow \ell ^+\ell ^-$$ Z → ℓ + ℓ - decay channel ( $$\ell =e,\mu$$ ℓ = e , μ ) as a function of four observables: the dijet invariant mass, the rapidity interval spanned by the two jets, the signed azimuthal angle between the two jets, and the transverse momentum of the dilepton pair. The data are corrected for the effects of detector inefficiency and resolution and are sufficiently precise to distinguish between different state-of-the-art theoretical predictions calculated using Powheg+Pythia8 , Herwig7+Vbfnlo and Sherpa  2.2. The differential cross-sections are used to search for anomalous weak-boson self-interactions using a dimension-six effective field theory. The measurement of the signed azimuthal angle between the two jets is found to more »