Simultaneous low-temperature electrical resistivity and Hall effect measurements were performed on single-crystalline Bi2Se3 under applied pressures up to 50 GPa. As a function of pressure, superconductivity is observed to onset above 11 GPa with a transition temperature Tc and upper critical field Hc2 that both increase with pressure up to 30 GPa, where they reach maximum values of 7 K and 4 T, respectively. Upon further pressure increase, Tc remains anomalously constant up to the highest achieved pressure. Conversely, the carrier concentration increases continuously with pressure, including a tenfold increase over the pressure range where Tc remains constant. Together with a quasilinear temperature dependence of Hc2 that exceeds the orbital and Pauli limits, the anomalously stagnant pressure dependence of Tc points to an unconventional pressure-induced pairing state in Bi2Se3 that is unique among the superconducting topological insulators.