Giant shell CdSe/CdS quantum dots are bright and flexible emitters, with near-unity quantum yield and suppressed blinking, but their single photon purity is reduced by efficient multiexcitonic emission. We report the observation, at the single dot level, of a large blueshift of the photoluminescence biexciton spectrum (24 ± 5 nm over a sample of 32 dots) for pure-phase wurtzite quantum dots. By spectral filtering, we demonstrate a 2.3 times reduction of the biexciton quantum yield relative to the exciton emission, while preserving as much as 60% of the exciton single photon emission, thus improving the purity from g2(0) = 0.07 ± 0.01 to g2(0) = 0.03 ± 0.01. At a larger pump fluency, spectral purification is even more effective with up to a 6.6 times reduction in g2(0), which is due to the suppression of higher order excitons and shell states experiencing even larger blueshifts. Our results indicate the potential for the synthesis of engineered giant shell quantum dots, with further increased biexciton blueshifts, for quantum optical applications requiring both high purity and brightness.