We report on the first pointed X-ray observations with XMM-Newton and RXTE satellites of the X-ray source RX J0757.0+6306 = HT Cam. We detect a strong 515 s X-ray modulation confirming the optical photometric period found in 1998, which definitively assigns this source to the intermediate polar class of magnetic cataclysmic variables. The lack of orbital sidebands in the X-rays indicates that the X-ray period is the spin period of the accreting white dwarf. Simultaneous ultraviolet and optical B-band photometry acquired with the XMM-Newton Optical Monitor and coordinated optical UBVRI photometric data acquired at the Nordic Optical Telescope (La Palma) show that the optical pulse is in phase with the X-rays and hence originates in the magnetically-confined accretion flow. The lack of ultraviolet spin modulation suggests that accretion-induced heating on the white dwarf surface is not important in this source. Spectral analyses of XMM-Newton EPIC and RGS data show that HT Cam has a multi-temperature spectrum and, contrary to most intermediate polars, it does not suffer from strong absorption. With its 86 min orbital period, HT Cam is the third confirmed system of this class below the 2-3 h period gap accreting at a low rate.