G-quadruplex (or G4) structures are non-canonical DNA structures that form in guanine-rich 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 (CMG) stalls at a leading strand G4 structure. Second, the DHX36 helicase mediates the bypass of the CMG past the intact G4 structure, which allows approach of the leading strand to the G4. Third, G4 structure unwinding by the FANCJ helicase enables the DNA polymerase to synthesize past the G4 motif. A G4 on the lagging strand template does not stall CMG, but still requires active DNA replication for unwinding. DHX36 and FANCJ have partially redundant roles, conferring robustness to this pathway. Our data reveal a novel genome maintenance pathway that promotes faithful G4 replication thereby avoiding genome instability.