We report on the ultra-high rate of photodegradation of organic dyes under visible light illumination on Ag2O-nanoparticle-decorated (NP) porous pure B-phase TiO2 (TiO2(B)) nanorods (NRs) grown by a solvothermal route. The as-grown TiO2(B) NRs are found to be nanoporous in nature and the Ag2O NPs are uniformly decorated over its surface, since most of the pores work as nucleation sites for the growth of Ag2O NPs. The effective band gap of the TiO2(B)/Ag2O heterostructure (HS), with a weight ratio of 1:1, has been significantly reduced to 1.68 eV from the pure TiO2(B) band gap of 2.8 eV. Steady state and time-resolved photoluminescence (PL) studies show the reduced intensity of visible PL and slower recombination dynamics in the HS samples. The photocatalytic degradation efficiency of the TiO2(B)/Ag2O HS has been investigated using aqueous methyl orange and methylene blue as reference dyes under visible light (390-800 nm) irradiation. It is found that photodegradation by the TiO2(B)/Ag2O HS is about one order of magnitude higher than that of bare TiO2(B) NRs and Ag2O NPs. The optimized TiO2(B)/Ag2O HS exhibited the highest photocatalytic efficiency, with 88.2% degradation for 30 min irradiation. The corresponding first order degradation rate constant is 0.071 min(-1), which is four times higher than the reported values. Furthermore, cyclic stability studies show the high stability of the HS photocatalyst for up to four cycles of use. The major improvement in photocatalytic efficiency has been explained on the basis of enhanced visible light absorption and band-bending-induced efficient charge separation in the HS. Our results demonstrate the long-term stability and superiority of the TiO2(B)/Ag2O HS over the bare TiO2(B) NRs and other TiO2-based photocatalysts for its cutting edge application in hydrogen production and environmental cleaning driven by solar light photocatalysis.