The Higgs-Dilaton model is able to produce an early inflationary expansion followed by a dark energy dominated era responsible for the late time acceleration of the Universe. At tree level, the model predicts a small tensor-to-scalar ratio (0.0021 <= r <= 0.0034), a tiny negative running of the spectral tilt (-0.00057 <= dn(s)/d ln k <= -0.00034) and a nontrivial consistency relation between the spectral tilt of scalar perturbations and the dark energy equation of state, which turns out to be close to a cosmological constant (0 <= 1 + w(DE) <= 0.014). We reconsider the validity of these predictions in the vicinity of the critical value of the Higgs self-coupling giving rise to an inflection point in the inflationary potential. The value of the inflationary observables in this case strongly depends on the parameters of the model. The tensor-to-scalar ratio can be large [ r similar to O(0.1)] and notably exceed its tree-level value. If that happens, the running of the scalar tilt becomes positive and rather big [dn(s)/d ln k similar to O(0.01)] and the equation-of-state parameter of dark energy can significantly differ from a cosmological constant [1 + w(DE) similar to O(0.1)].