A strong anti-Stokes Raman signal, from the vibrational Q(1) transition of hydrogen, is generated in gas-filled hollow-core photonic crystal fiber. To be efficient, this process requires phase-matching, which is not automatically provided since the group velocity dispersion is typically non-zero and--inside a fiber--cannot be compensated for using a crossed-beam geometry. Phase-matching can however be arranged by exploiting the different dispersion profiles of higher-order modes. We demonstrate the generation of first and second anti-Stokes signals in higher-order modes by pumping with an appropriate mixture of fundamental and a higher-order modes, synthesized using a spatial light modulator. Conversion efficiencies as high as 5.3% are achieved from the pump to the first anti-Stokes band.