Vector light gains an increasing interest due to its exotic spatial polarization structure texture, which is governed by the intramodal phase of two orthogonal polarization components, and, in particular, has shown great potential in optical metrology. We present and demonstrate experimentally a novel laser interferometric technique fed by a vector sensing beam. The phase variation of the interferometer is first mapped into the intramodal phase of the sensing beam. Then, by in-situ characterizing the vectorial polarization state of the sensing beam via spatial Stokes tomography, a precision phase estimation approaching standard-quantum or Heisenberg (by feeding a N00N state) limit can be achieved in arbitrary phase ranges including insensitive regions.