We present cosmological solutions for a graviton-plus-dilaton system coupled to a perfect fluid source, including quadratic curvature corrections. We show that, even in the absence of a dilaton self-interaction potential, isotropic superinflation (H > 0) can be realized for a wide range of equations of state, which includes in particular the ordinary cases of dust matter and radiation. It is found that in this context inflation can be produced more efficiently than in previous superinflationary models based on the contraction of internal dimensions.