We explore the excitation of plasmons in 3D plasmon crystal metamaterials and report the observation of a delocalized plasmon mode, which provides extremely high spectral sensitivity (>2600 nm per refractive index unit (RIU) change), outperforming all plasmonic counterparts excited in 2D nanoscale geometries, as well as a prominent phase-sensitive response (>3*10(4) deg. of phase per RIU). Combined with a large surface for bioimmobilization provided by the 3D matrix, the proposed sensor architecture promises a new important landmark in the advancement of plasmonic biosensing technology.