A new polynomial-rooting-based algorithm with two parallel uniform linear arrays of dipole-triads is proposed for estimating two dimensional (2-D) Directions of arrival (DOAs) of multiple source signals. The proposed algorithm derives the direction cosine estimates along xaxis and y-axis, successively, from polynomial roots and eigenvectors associated with the roots. When the intervector sensor spacing exceeds a half-wavelength, the derived direction cosine estimates are ambiguous. Fortunately, the eigenvectors can also be straightforwardly used to yield dipole-triad's manifold estimates, thus the ambiguities can be resolved using the manifold estimates. Unlike other existing ESPRIT-based algorithm, our algorithm can achieve automatic pairing without any additional processing. Numerical examples are presented to verify the effectiveness of the proposed method.