Pevtsov et al. recently showed that the luminosity of solar and stellar X-rays from closed magnetic structures scales nearly linearly with magnetic flux over 12 decades. We show here that the total power available to accelerate the solar wind also scales linearly with magnetic flux, provided that its sources inject a roughly constant energy per particle prior to losses from heat conducted by electrons into radiation. Using a recently developed model of the solar wind energy source and particle source, we calculate the available solar wind power and convert it into an equivalent X-ray luminosity to explore whether the same process that drives solar wind may also power coronal heating. The quantitative results agree remarkably well with the Pevtsov et al. X-ray observations and with GOES X-ray observations over almost two solar cycles from 1985 to 2004. The model for the solar wind energy and particle source relies on the continual reconfiguration of the supergranular network through the emergence of small bipolar or more complex closed magnetic fields. This naturally leads to an energy flux proportional to field strength on large-scale field structures with field strengths larger than the emerging flux. We conclude that the sources of energy for the solar wind and coronal heating are linked, likely through the emergence of new magnetic flux that continually reconfigures large-scale solar magnetic fields and powers and heats the corona.