Surface plasmon resonance (SPR) sensors can reach the quantum noise limit of the optical readout field in various configurations. We demonstrate that two-mode intensity squeezed states produce a further enhancement in sensitivity compared with a classical optical readout when the quantum noise is used to transduce an SPR sensor signal in the Kretschmann configuration. The quantum noise reduction between the twin beams when incident at an angle away from the plasmonic resonance, combined with quantum noise resulting from quantum anticorrelations when on resonance, results in an effective SPR-mediated modulation that yields a measured sensitivity 5 dB better than that with a classical optical readout in this configuration. The theoretical potential of this technique points to resolving particle concentrations with more accuracy than is possible via classical approaches to optical transduction.