We study a model of quintessential inflation constructed in R2-modified gravity with a non-minimally coupled scalar field, in the Palatini formalism. Our non-minimal inflaton field is characterised by a simple exponential potential. We find that successful quintessential inflation can be achieved with no fine-tuning of the model parameters. Predictions of the characteristics of dark energy will be tested by observations in the near future, while contrasting with existing observations provides insights on the modified gravity background, such as the value of the non-minimal coupling and its running.