It is well-known that the Dixon resultant implicitizes exactly a general tensor product surface. We show that a minor of the Dixon resultant matrix can also implicitize exactly. This occurs when the monomial support of the surface parametrization is a rectangle missing at most one sub-rectangle at each of its its corners. Unlike the Sylvester dialytic method, this way of finding the implicit equation in determinant form is automatic, in bracket form, and uses much smaller matrices.