Precise control of the dispersion landscape is of crucial importance if optical fibers are to be successfully used for the generation of three-photon states of light-the inverse of third-harmonic generation (THG). Here we report gas-tuning of intermodal phase-matched THG in sub-micron-diameter tapered optical fiber. By adjusting the pressure of the surrounding argon gas up to 50 bars, intermodally phase-matched third-harmonic light can be generated for pump wavelengths within a 15 nm range around 1.38 μm. We also measure the infrared fluorescence generated in the fiber when pumped in the visible and estimate that the accidental coincidence rate in this signal is lower than the predicted detection rate of photon triplets.