An exact solution for the boundary problem of temporal correlations of light multiply scattered from a medium occupying a half space is found by means of the Wiener-Hopf method, taking into account single-scattering anisotropy. Within the P1 approximation a universal initial decay rate of the temporal correlation function is obtained. For larger time intervals a higher single-scattering anisotropy yields a higher decay rate contrary to predictions of the diffusion approximation. Within the P2 approximation, which takes account of the first- and second-order Legendre polynomials, the solution obtained becomes universal in an expanded temporal range and agrees rather well with the known measurement data.