Material emitted as ejecta from ONe novae outbursts is observed to be rich in elements as heavy as Ca. The bottleneck for the synthesis of elements beyond sulphur is the (30)P(p,γ)(31)S reaction. Its reaction rate is, however, not well determined due to uncertainties in the properties of key resonances in the burning regime. In the present study, gamma-ray transitions are reported for the first time from all key states in (31)S relevant for the (30)P(p,γ)(31)S reaction. The spins and parity of these resonances have been deduced, and energies have been measured with the highest precision to date. The uncertainty in the estimated (30)P(p,γ)(31)S reaction rate has been drastically reduced. The rate using this new information is typically higher than previous estimates based on earlier experimental data, implying a higher flux of material processed to high-Z elements in novae, but it is in good agreement with predictions using the Hauser-Feshbach approach at higher burning temperatures.