The two-flavour Nambu-Jona-Lasinio model with N components is studied in curved spacetime at finite temperature and density in the leading 1/N expansion. In four spacetime dimensions the model exhibits a first-order phase transition for positive curvature. Whereas in flat space an increase in temperature induces a second-order phase transition even at finite density, in curved space the transition becomes first order. We obtain the phase boundary in density-temperature plane and exhibit its behaviour with changing curvature. A three-dimensional plot of the phase boundary in µ-T-R space is drawn.