JWST has revealed a class of numerous, extremely compact sources with rest-frame red optical/near-infrared (NIR) and blue ultraviolet (UV) colours nicknamed ‘little red dots’. We present one of the highest signal-to-noise ratio JWST NIRSpec prism spectra of a little red dot, J0647_1045 at z = 4.5319 ± 0.0001, and examine its NIRCam morphology to differentiate the origin of the UV and optical/NIR emission and elucidate the nature of the little red dot phenomenon. J0647_1045 is unresolved (re ≲ 0.17 kpc) in the three NIRCam long-wavelength filters but significantly extended (re = 0.45 ± 0.06 kpc) in the three short-wavelength filters, indicating a red compact source in a blue star-forming galaxy. The spectral continuum shows a clear change in slope, from blue in the optical/UV to red in the rest-frame optical/NIR, which is consistent with two distinct components fit by power laws with different attenuations: AV = 0.38 ± 0.01 (UV) and AV = 5.61 ± 0.04 (optical/NIR). Fitting the Hα line requires both broad (full width at half maximum of ∼4300 ± 100 km s−1) and narrow components, but none of the other emission lines, including Hβ, show evidence of broadness. We calculated AV = 0.9 ± 0.4 from the Balmer decrement using narrow Hα and Hβ and AV > 4.1 ± 0.1 from broad Hα and an upper limit on broad Hβ, which is consistent with blue and red continuum attenuation, respectively. Based on a single-epoch Hα line width, the mass of the central black hole is 8−0.4+0.5 × 108 M⊙. Our findings are consistent with a multi-component model, in which the optical/NIR and broad lines arise from a highly obscured, spatially unresolved region, likely a relatively massive active galactic nucleus, while the less obscured UV continuum and narrow lines arise, at least partly, from a small but spatially resolved star-forming host galaxy.