MKT1 is a pleiotropic stress response gene identified by several quantitative trait studies with MKT189G as a causal variant, contributing to growth advantage in multiple stress environments. MKT1 has been shown to regulate HO endonuclease posttranscriptionally via the Pbp1–Pab1 complex. RNA-binding protein Puf3 modulates a set of nuclear-encoded mitochondrial transcripts whose expression was found to be affected by MKT1 alleles. This study attempts to relate the MKT1 allele-derived growth advantage with the stability of Puf3 targets during stress and elucidate the roles of Pbp1 and Puf3 in this mechanism. Our results showed that the growth advantage of the MKT189G allele in cycloheximide and H2O2 was PBP1-dependent, whereas in 4-nitroquinoline 1-oxide, the growth advantage was dependent on both PUF3 and PBP1. We compared the messenger RNA decay kinetics of a set of Puf3 targets in multiple stress environments to understand the allele-specific regulation by MKT1. In oxidative stress, the MKT189G allele modulated the differential expression of nuclear-encoded mitochondrial genes in a PBP1- and PUF3-dependent manner. Additionally, MKT189G stabilised Puf3 targets, namely, COX17, MRS1 and RDL2, in an allele and stress-specific manner. Our results showed that COX17, MRS1 and RDL2 had a stress-specific response in stress environments, with the MKT189G allele contributing to better growth; this response was both PBP1- and PUF3-dependent. Our results indicate that the common allele, MKT189G, regulates stress responses by differentially stabilising Puf3-target mitochondrial genes, which allows for the strain’s better growth in stress environments.