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The measurement of the triple gauge couplings (TGCs) is a central part ofdiboson studies at the LHC. In this letter we consider the $Z\gamma$ processand include anomalous TGCs (aTGCs) in the event generation atnext-to-next-to-leading order QCD accuracy (NNLO+PS) within the MiNNLO$_{\rmPS}$ framework. While our implementation is fully general and applies to both$Z\to \ell^+\ell^-$ and $Z\to \nu\bar\nu$ decays, we focus here on the$\nu\bar\nu\gamma$ final state. After validation of our simulation of$\nu\bar\nu\gamma$ events, for which NNLO+PS accuracy is achieved for the firsttime, the effects of aTGCs on various distributions are studied. Moreover, weshow the relevance of NNLO+PS accuracy for the $\nu\bar\nu\gamma$ background tophoton plus missing energy signatures in dark-matter searches, and we compareMiNNLO$_{\rm PS}$ predictions for $\nu\bar\nu\gamma$ production to recent 13TeV data.

Anomalous couplings in $Z\gamma$ events at NNLO+PS and improving $\nu\bar\nu\gamma$ backgrounds in dark-matter searches