The yeast Komagataella phaffii (Pichia pastoris) is currently considered a versatile and highly efficient host for recombinant protein production (RPP). Interestingly, the regulated application of specific stress factors as part of bioprocess engineering strategies has proven potential for increasing the production of recombinant products. This study aims to evaluate the impact of controlled oxygen‐limiting conditions on the performance of K. phaffii bioprocesses for RPP in combination with the specific growth rate (μ) in fed‐batch cultivations. In this work, Candida rugosa lipase 1 (Crl1) production, regulated by the constitutive GAP promoter, growing at different nominal μ (0.030, 0.065, 0.100 and 0.120 h−1) under both normoxic and hypoxic conditions in carbon‐limiting fed‐batch cultures is analysed. Hypoxic fermentations were controlled at a target respiratory quotient (RQ) of 1.4, with excellent performance, using an innovative automated control based on the stirring rate as the manipulated variable developed during this study. The results conclude that oxygen limitation positively affects bioprocess efficiency under all growing conditions compared. The shift from respiratory to respiro‐fermentative metabolism increases bioprocess productivity by up to twofold for the specific growth rates evaluated. Moreover, the specific product generation rate (qp) increases linearly with μ, regardless of oxygen availability. Furthermore, this hypoxic boosting effect was also observed in the production of Candida antarctica lipase B (CalB) and pro‐Rhizopus oryzae lipase (proRol), thus proving the synergic effect of kinetic and physiological stress control. Finally, the Crl1 production scale‐up was conducted successfully, confirming the strategy's scalability and the robustness of the results obtained at the bench‐scale level.