  We present the results of the first Dalitz plot analysis of the decay
$D^{0}\to K^{-}\pi^{+}\eta$. The analysis is performed on a data set
corresponding to an integrated luminosity of 953 $\rm{fb}^{-1}$ collected by
the Belle detector at the asymmetric-energy $e^{+}e^{-}$ KEKB collider. The
Dalitz plot is well described by a combination of the six resonant decay
channels $\bar{K}^{*}(892)^0\eta$, $K^{-}a_0(980)^+$, $K^{-}a_2(1320)^+$,
$\bar{K}^{*}(1410)^0\eta$, $K^{*}(1680)^-\pi^{+}$ and $K_2^{*}(1980)^-\pi^{+}$,
together with $K\pi$ and $K\eta$ S-wave components. The decays
$K^{*}(1680)^{-}\to K^{-}\eta$ and $K_{2}^{*}(1980)^{-}\to K^{-}\eta$ are
observed for the first time. We measure ratio of the branching fractions,
$\frac{\mathcal{B}(D^{0}\to K^{-}\pi^{+}\eta)}{\mathcal{B}(D^{0}\to
K^{-}\pi^{+})}=0.500\pm0.002{\rm(stat)}\pm0.020{\rm(syst)}\pm0.003{\rm
(\mathcal{B}_{PDG})}$. Using the Dalitz fit result, the ratio
$\frac{\mathcal{B}(K^{*}(1680)\to K\eta)}{\mathcal{B}(K^{*}(1680)\to K\pi)}$ is
measured to be
$0.11\pm0.02{\rm(stat)}^{+0.06}_{-0.04}{\rm(syst)}\pm0.04{\rm(\mathcal{B}_{\text{PDG}})}$;
this is much lower than the theoretical expectations ($\approx1$) made under
the assumption that $K^{*}(1680)$ is a pure $1^{3}D_1$ state. The product
branching fraction $\mathcal{B}(D^0\to [K_2^{*}(1980)^-\to
K^{-}\eta]\pi^{+})=(2.2^{+1.7}_{-1.9})\times10^{-4}$ is determined. In
addition, the $\pi\eta^{\prime}$ contribution to the $a_0(980)^{\pm}$ resonance
shape is confirmed with 10.1$\sigma$ statistical significance using the
three-channel Flatt\'{e} model. We also measure
$\mathcal{B}(D^0\to\bar{K}^{*}(892)^0\eta)=(1.41^{+0.13}_{-0.12})\%$. This is
consistent with, and more precise than, the current world average
$(1.02\pm0.30)\%$, deviates with a significance of more than $3\sigma$ from the
theoretical predictions of (0.51-0.92)%.
