The influence of a CdSexS1-x interfacial alloyed layer on the photophysical properties of core/shell CdSe/CdS nanocrystal quantum dots (QDs) is investigated by comparing reference QDs with a sharp core/shell interface to alloyed structures with an intermediate CdSexS1-x layer at the core/shell interface. To fully realize the structural contrast, we have developed two novel synthetic approaches: a method for fast CdS-shell growth, which results in an abrupt core/shell boundary (no intentional or unintentional alloying), and a method for depositing a CdSexS1-x alloy layer of controlled composition onto the CdSe core prior to the growth of the CdS shell. Both types of QDs possess similar size-dependent single-exciton properties (photoluminescence energy, quantum yield, and decay lifetime). However the alloyed QDs show a significantly longer biexciton lifetime and up to a 3-fold increase in the biexciton emission efficiency compared to the reference samples. These results provide direct evidence that the structure of the QD interface has a significant effect on the rate of nonradiative Auger recombination, which dominates biexciton decay. We also observe that the energy gradient at the core-shell interface introduced by the alloyed layer accelerates hole trapping from the shell to the core states, which results in suppression of shell emission. This comparative study offers practical guidelines for controlling multicarrier Auger recombination without a significant effect on either spectral or dynamical properties of single excitons. The proposed strategy should be applicable to QDs of a variety of compositions (including, e.g., infrared-emitting QDs) and can benefit numerous applications from light emitting diodes and lasers to photodetectors and photovoltaics.