CuxBi2Se3 was recently proposed as a promising candidate for time-reversal-invariant topological superconductors[1]. In this work, we argue that the unusual anisotropy of the Knight shift observed by Zheng[2], taken together with specific heat measurements, provides strong support for an unconventional odd-parity pairing in the two-dimensional E_u representation of the D3d crystal point group[1], which spontaneously breaks the three-fold rotational symmetry of the crystal, leading to a subsidiary nematic order. We predict that the spin-orbit interaction associated with hexagonal warping plays a crucial role in pinning the two-component order parameter and makes the superconducting state fully-gapped, leading to a topological superconductor. Experimental signatures of the E_u pairing related to the nematic order are discussed.