We report on the population of point sources discovered during an 18.5 ks Chandra ACIS-S observation of the Sombrero galaxy. We present the luminosity function and the spectra of the six brightest sources, consider correlations with globular clusters (GCs) and with planetary nebulae, and study the galaxy's population of very soft sources. We detected 122 sources. Twenty-two sources are identified as very soft; of these, five appear to be classical luminous supersoft X-ray sources (SSSs), while 17 may belong to the slightly harder class referred to as quasi-soft (QSSs). There is an overdensity of very soft sources within 2 kpc of the nucleus, which is itself the brightest X-ray source. Very soft sources are also found in the disk and halo, with one QSS in a globular cluster (GC). This source is somewhat harder than most SSSs; the energy distribution of its photons is consistent with what is expected from an accreting intermediate-mass black hole. Several sources in the Sombrero's halo are good candidates for SSS models in which the accretor is a nuclear-burning white dwarf. In total, 32 X-ray sources are associated with GCs. The majority of sources with luminosity greater than 10 38 ergs s À1 are in GCs. These results for M104, an Sa galaxy, are similar to what has been found for elliptical galaxies and for the latetype spiral M31. We find that those optically bright GCs with X-ray sources house only the brightest X-ray sources. We find that, in common with other galaxies, there appears to be a positive connection between young (metal-rich) GCs and X-ray sources but that the brightest X-ray sources are equally likely to be in metal-poor GCs. The luminosity function of X-ray sources in GCs has a cut-off near the Eddington luminosity for a 1.4 M object. We propose a model that can explain the trends seen in the data sets from the Sombrero and other galaxies. Thermal timescale mass transfer can occur in some of the younger clusters in which the turnoff mass is slightly greater than 0.8 M ; multiplicity may play a role in some of the most massive clusters; accretion from giant stars may be the dominant mechanism in some older, less massive and less centrally concentrated clusters. Key elements of the model can be tested.