We have investigated the action of the human DNA polymerase ε (hpol ε) and η (hpol η) catalytic cores on G-quadruplex (G4) DNA substrates derived from the promoter of the c-MYC proto-oncogene. The translesion enzyme hpol η exhibits a 6.2-fold preference for binding to G4 DNA over non-G4 DNA, while hpol ε binds both G4 and non-G4 substrates with nearly equal affinity. Kinetic analysis of single-nucleotide insertion by hpol η reveals that it is able to maintain >25% activity on G4 substrates compared to non-G4 DNA substrates, even when the primer template junction is positioned directly adjacent to G22 (the first tetrad-associated guanine in the c-MYC G4 motif). Surprisingly, hpol η fidelity increases ~15-fold when copying G22. By way of comparison, hpol ε retains ~4% activity and has a 33-fold decrease in fidelity when copying G22. The fidelity of hpol η is ~100-fold greater than that of hpol ε when comparing the misinsertion frequencies of the two enzymes opposite a tetrad-associated guanine. The kinetic differences observed for the B- and Y-family pols on G4 DNA support a model in which a simple kinetic switch between replicative and TLS pols could help govern fork progress during G4 DNA replication.