Enzymatic inhibition by product molecules is an important and widespread phenomenon. We describe an approach to study product inhibition at the single-molecule level. Individual HRP molecules are trapped within surface-tethered lipid vesicles, and their reaction with a fluorogenic substrate is probed. While the substrate readily penetrates into the vesicles, the charged product (resorufin) gets trapped and accumulates inside the vesicles. Surprisingly, individual enzyme molecules are found to stall when a few tens of product molecules accumulate. Bulk enzymology experiments verify that the enzyme is noncompetitively inhibited by resorufin. The initial reaction velocity of individual enzyme molecules and the number of product molecules required for their complete inhibition are broadly distributed and dynamically disordered. The two seemingly unrelated parameters, however, are found to be substantially correlated with each other in each enzyme molecule and over long times. These results suggest that, as a way to counter disorder, enzymes have evolved the means to correlate fluctuations at structurally distinct functional sites.