Noble metal nanoparticles support localized surface plasmon resonances (LSPRs) that are extremely sensitive to the local dielectric properties of the environment within distances up to 10-100 nm from the metal surface. The significant overlap between the sensing volume of the nanoparticles and the size of biological macromolecules has made LSPR biosensing a key field for the application of plasmonics. Recent advancements in evaluating plasmonic refractometric sensors have suggested that the phase detection of light can surpass the sensitivity of standard intensity-based detection techniques. Here, we experimentally confirm that the phase of light can be used to precisely track local refractive index changes induced by biomolecular reactions, even for dilute and layers of short-range-ordered plasmonic nanoparticles. In particular, we demonstrate that the sensitivity can be enhanced by tuning in to a zero reflection condition, in which an abrupt phase flip of the reflected light is achieved. Using a cost-effective interference fringe tracking technique, we demonstrate that phase measurements yield an approximately one order of magnitude larger relative shift compared with traditional LSPR measurements for the model system of NeutrAvidin binding to biotinylated nanodisks.