Photoluminescence phenomena normally obey Stokes' law of luminescence according to which the emitted photon energy is typically lower than its excitation counterparts. Here we show that carbon nanotubes break this rule under one-photon excitation conditions. We found that the carbon nanotubes exhibit efficient near-infrared photoluminescence upon photoexcitation even at an energy lying 4100-200 meV below that of the emission at room temperature. This apparently anomalous phenomenon is attributed to efficient one-phonon-assisted up-conversion processes resulting from unique excited-state dynamics emerging in an individual carbon nanotube with accidentally or intentionally embedded localized states. These findings may open new doors for energy harvesting, optoelectronics and deep-tissue photoluminescence imaging in the near-infrared optical range.