This paper derives a novel pilot-aided phase and channel estimation algorithm for multiple-input multiple-output (MIMO) systems with phase noise and quasi-static channel fading. Our novel approach allows, for the first time, carrier phase estimation and recovery to be performed before full channel estimation. This in turn enables the channel estimation to be calculated using the whole frame, significantly improving its accuracy. The proposed algorithm is a sequential combination of several linear algorithms, which greatly reduces the computational complexity. Moreover, we also derive, for the first time, the Cramer-Rao lower bound (CRLB) for a MIMO system, where phase noise is estimated using only angular information. Our numerical results show that the performance of our phase estimation algorithm is close to the proposed CRLB. Moreover, when compared with the conventional Kalman based algorithms, our proposed algorithm significantly improves the system BER performance.