The origin of the different sub-types of hydrogen-rich (Type II) supernovae and their connection to stellar and binary physics remains uncertain. Type II-L supernovae are often believed to originate from stars that have lost parts of their hydrogen-rich envelopes. However, such models struggle to reproduce all features of the observed light curves. We propose an alternative scenario by considering the naturally induced pulsations of red supergiants (RSGs) towards the end of their evolution. To investigate this, we self-consistently model these pulsations of RSGs in 1D. The pulsations are naturally induced by a κγ-mechanism in the envelope. The models are then exploded at different phases during the pulsation cycle to calculate the light curve of the resulting supernova. We find that for the same progenitor star, the pulsations significantly alter the envelope structure and the resulting supernova light curve, as well as the location of the progenitor in the Hertzsprung-Russell diagram, depending on the pulsation phase. The strength of these effects increases with increasing RSG mass. We show that some observed diversity in the light curves of Type II supernovae may be explained by considering the pulsations of RSGs. We discuss our model in the context of two recent supernovae, SN 2023ixf and SN 2024ggi, which both show signs of a pulsating progenitor star. In both cases, considering the explosion of pulsating RSGs offers an explanation for their light curve.