Autocorrelation is a common method to estimate the duration of ultrashort laser pulses. In the ultraviolet (UV) regime it is challenging to employ the process of second-harmonic generation, most prominently due to absorption in nonlinear crystals at very short wavelengths. Here we show how to utilize spontaneous parametric down-conversion (SPDC) to generate an autocorrelation signal in the infrared (IR) for UV pulses. Our method utilizes the nth-order emission of the SPDC process, which occurs for low pumping powers proportional to the nth power of the UV intensity. Thus, counting 2n down-converted photons directly yields the nth-order autocorrelation. The method, now with detection of near-IR photons, is applied to the first direct measurement of ultrashort UV pulses circulating inside a UV enhancement cavity.