The invention relates to a tire having a rubber tread of a cap/base configuration composed of a composite of a silica-rich tread cap layer running surface, and an underlying transition zone composite of a carbon black-rich intermediate layer positioned between the tread cap layer and a tread base layer. The combination of intermediate layer and base layer provide a beneficial graduated stiffness between the tread cap layer and the tire carcass. Significantly, the transition zone composite enables a significantly thicker carbon-black rich portion of the tread composite and an associated thinner silica-rich tread cap running surface. In one aspect, the intermediate layer of the transition zone composite can extend to and include a bottom portion of at least two of the grooves of said tread cap layer to support an associated tread lug therebetween.