Globular clusters (GCs) are dense star clusters found in all massive galaxies. Recent work has established that they follow a tight relation between their internal stellar velocity dispersion σ and luminosity, enabling accurate distance measurements. In this work, we aim to apply this GC velocity dispersion (GCVD) distance method to measure the distance to M 104 (NGC 4594, the Sombrero galaxy). We have measured internal stellar velocity dispersions for 85 globular clusters (GCs) and one ultra-compact dwarf galaxy around M 104 using high-resolution multi-object integrated-light spectroscopy with FLAMES/GIRAFFE on the Very Large Telescope. The measured velocity dispersions range from σ=4−30 km s, with a mean uncertainty of ∆σ=2.5 km s. For a subset of 77 GCs with V-band magnitudes and reliable velocity dispersion measurements above σ>4 km s, we constructed the MV- σ relation to measure the distance to M 104, finding D=9.00±0.29 (stat.) ±0.26 (sys.) Mpc. The GCs follow the Milky Way and M 31 MV−σ relation closely, with the exception of the luminous ultra-compact dwarf SUCD1, which is nearly one magnitude brighter than the mean relation. 29 GCs in the sample have sizes determined from Hubble Space Telescope imaging which allowed us to determine their masses and V-band dynamical mass-to-light ratios (M/L). We find a mean <M/LV>=2.6M☉/L☉ for the luminous ( MV<−8 mag) M 104 GCs, which is higher than the Milky Way GCs, but is reminiscent of the brightest GCs in Centaurus A. With the exception of SUCD1, the GCs of M 104 follow the GCVD relation irrespective of their mass-to-light ratio.