Excitons in semiconductor quantum dots (QDs) feature high values of the two-photon absorption cross-sections (TPACSs), enabling applications of two-photon-excited photoluminescence (TPE PL) of QDs in biosensing and nonlinear optoelectronics. However, efficient TPE PL of QDs requires high-intensity laser fields, which limits these applications. There are two possible ways to increase the TPE PL of QDs: by increasing their photoluminescence quantum yield (PLQY) or by further increasing the TPACS. Plasmonic nanoparticles (PNPs) may act as open nanocavities for increasing the PLQY via the Purcell effect, but this enhancement is strictly limited by the maximum possible PLQY value of 100%. Here we directly investigated the effect of PNPs on the effective TPACS of excitons in QDs. We have found that effective TPACS of excitons in a QD-PMMA thin film can be increased by a factor of up to 12 near the linearly excited gold nanorods (GNRs). Using gold nanospheres (GNSs), in which plasmons cannot be excited in the infrared range, as a control system, we have shown that, although both GNSs and GNRs increase the recombination rate of excitons, the TPACS is increased only in the case of GNRs. We believe that the observed effect of TPACS enhancement is a result of the nonlinear interaction of the plasmons in GNRs with excitons in QDs, which we have supported by numerical simulations. The results show the way to the rational design of the spectral features of plasmon-exciton hybrids for using them in biosensing and nonlinear optoelectronics.