Quantum emitters are an integral component for a broad range of quantum technologies including quantum communication, quantum repeaters, and linear optical quantum computation. Solid-state color centers are promising candidates for scalable quantum optics due to their long coherence time and small inhomogeneous broadening. However, once excited, color centers often decay through phonon-assisted processes, limiting the efficiency of single photon generation and photon mediated entanglement generation. Herein, we demonstrate strong enhancement of spontaneous emission rate of a single silicon-vacancy center in diamond embedded within a monolithic optical cavity, reaching a regime where the excited state lifetime is dominated by spontaneous emission into the cavity mode. We observe 10-fold lifetime reduction and 42-fold enhancement in emission intensity when the cavity is tuned into resonance with the optical transition of a single silicon-vacancy center, corresponding to 90% of the excited state energy decay occurring through spontaneous emission into the cavity mode. We also demonstrate the largest to date coupling strength ($g/2\pi=4.9\pm0.3 GHz$) and cooperativity ($C=1.4$) for color-center-based cavity quantum electrodynamics systems, bringing the system closer to the strong coupling regime.