Graphene-plasmonic hybrid platforms have attracted an enormous amount of interest in surface-enhanced Raman scattering (SERS); however, the mechanism of employing graphene is still ambiguous, so clarification about the complex interaction among molecules, graphene, and plasmon processes is urgently needed. We report that the number of graphene layers controlled the plasmon-driven, surface-catalyzed reaction that converts para-aminothiophenol (PATP)-to-p,p9-dimercaptoazobenzene (DMAB) on chemically inert, graphene-coated, silver bowtie nanoantenna arrays. The catalytic reaction was monitored by SERS, which revealed that the catalytic reaction occurred on the chemical inertness monolayer graphene (1G)-coated silver nanostructures. The introduction of 1G enhances the plasmon-driven surface-catalyzed reaction of the conversion of PATP-to-p,p9-DMAB. The chemical reaction is suppressed by bilayer graphene. In the process of the catalytic reaction, the electron transfer from the PATP molecule to 1G-coated silver nanostructures. Subsequently, the transferred electrons on the graphene recombine with the hot-hole produced by the localized surface plasmon resonance of silver nanostructures. Then, a couple of PATP molecules lost electrons are catalyzed into the p,p9-DMAB molecule on the graphene surface. The experimental results were further supported by the finite-difference time-domain method and quantum chemical calculations.