Sources of pure and indistinguishable single-photons are critical for near-future optical quantum technologies. Recently, color centers hosted by two-dimensional hexagonal boron nitride (hBN) have emerged as a promising platform for high luminosity room temperature single-photon sources. Despite the brightness of the emitters, the spectrum is rather broad and the single-photon purity is not sufficient for practical quantum information processing. Here, we report integration of such a quantum emitter hosted by hBN into a tunable optical microcavity. A small mode volume of the order of λ3 allows us to Purcell enhance the fluorescence, with the observed excited state lifetime shortening. The cavity significantly narrows the spectrum and improves the single-photon purity by suppression of off-resonant noise. The complete device, including all optics, driving electronics, and control units, is compact and integrated in a small volume of 10 × 10 × 10 cm3, allowing for portable usage in mobile applications.