Abstract The Mukhanov–Sasaki equation is deduced from linear perturbations for a general scalar-tensor model with non-minimal coupling to curvature, to the Gauss–Bonnet invariant and non-minimal kinetic coupling to curvature. The general formulas for the power spectra of the primordial scalar and tensor fluctuations are obtained for arbitrary coupling functions. The results have been applied to models with power-law, exponential, natural and double-well potentials. It was found that the presence of these non-minimal couplings affect the inflationary observables leading to values favored by the latest observations, while some interesting results like sub-planckian symmetry breaking scale in natural inflation and sub-planckian v.e.v. of the scalar filed in the double-well potential were obtained. The consistency with the reheating process was discussed and some numerical cases were shown. The equivalence of the model to a sector of generalized Galileons was shown and the functions that establish the correspondence were found.