  The concept of Higgs inflation can be elegantly incorporated in the
Next-to-Minimal Supersymmetric Standard Model (NMSSM). A linear combination of
the two Higgs-doublet fields plays the role of the inflaton which is
non-minimally coupled to gravity. This non-minimal coupling appears in the
low-energy effective superpotential and changes the phenomenology at the
electroweak scale. While the field content of the inflation-inspired model is
the same as in the NMSSM, there is another contribution to the $\mu$ term in
addition to the vacuum expectation value of the singlet. We explore this
extended parameter space and point out scenarios with phenomenological
differences compared to the pure NMSSM. A special focus is set on the
electroweak vacuum stability and the parameter dependence of the Higgs and
neutralino sectors. We highlight regions which yield a SM-like $125\,$GeV Higgs
boson compatible with the experimental observations and are in accordance with
the limits from searches for additional Higgs bosons. Finally, we study the
impact of the non-minimal coupling to gravity on the Higgs mixing and in turn
on the decays of the Higgs bosons in this model.
