DNA polymerases (Pols) ε and δ perform the bulk of yeast leading- and lagging-strand DNA synthesis. Both Pols possess intrinsic proofreading exonucleases that edit errors during polymerization. Rare errors that elude proofreading are extended into duplex DNA and excised by the mismatch repair (MMR) system. Strains that lack Pol proofreading or MMR exhibit a 10- to 100-fold increase in spontaneous mutation rate (mutator phenotype), and inactivation of both Pol δ proofreading (pol3-01) and MMR is lethal due to replication error-induced extinction (EEX). It is unclear whether a similar synthetic lethal relationship exists between defects in Pol ε proofreading (pol2-4) and MMR. Using a plasmid-shuffling strategy in haploid Saccharomyces cerevisiae, we observed synthetic lethality of pol2-4 with alleles that completely abrogate MMR (msh2Δ, mlh1Δ, msh3Δ msh6Δ, or pms1Δ mlh3Δ) but not with partial MMR loss (msh3Δ, msh6Δ, pms1Δ, or mlh3Δ), indicating that high levels of unrepaired Pol ε errors drive extinction. However, variants that escape this error-induced extinction (eex mutants) frequently emerged. Five percent of pol2-4 msh2Δ eex mutants encoded second-site changes in Pol ε that reduced the pol2-4 mutator phenotype between 3- and 23-fold. The remaining eex alleles were extragenic to pol2-4. The locations of antimutator amino-acid changes in Pol ε and their effects on mutation spectra suggest multiple mechanisms of mutator suppression. Our data indicate that unrepaired leading- and lagging-strand polymerase errors drive extinction within a few cell divisions and suggest that there are polymerase-specific pathways of mutator suppression. The prevalence of suppressors extragenic to the Pol ε gene suggests that factors in addition to proofreading and MMR influence leading-strand DNA replication fidelity.