G-quadruplex (or G4) structures form in guanine-rich DNA sequences and threaten genome stability when not properly resolved. G4 unwinding occurs during S phase via an unknown mechanism. Using Xenopus egg extracts, we define a three-step G4 unwinding mechanism that acts during DNA replication. First, the replicative helicase composed of Cdc45, MCM2-7 and GINS (CMG) stalls at a leading strand G4 structure. Second, the DEAH-box helicase 36 (DHX36) mediates bypass of the CMG past the intact G4 structure, allowing approach of the leading strand to the G4. Third, G4 structure unwinding by the Fanconi anemia complementation group J helicase (FANCJ) enables DNA polymerase to synthesize past the G4 motif. A G4 on the lagging strand template does not stall CMG but still requires DNA replication for unwinding. DHX36 and FANCJ have partially redundant roles, conferring pathway robustness. This previously unknown genome maintenance pathway promotes faithful G4 replication, thereby avoiding genome instability.