G-quadruplexes (G4s) form throughout the genome and influence important cellular processes. Their deregulation can challenge DNA replication fork progression and threaten genome stability. Here, we demonstrate an unexpected role for the double-stranded DNA (dsDNA) translocase helicase-like transcription factor (HLTF) in responding to G4s. We show that HLTF, which is enriched at G4s in the human genome, can directly unfold G4s in vitro and uses this ATP-dependent translocase function to suppress G4 accumulation throughout the cell cycle. Additionally, MSH2 (a component of MutS heterodimers that bind G4s) and HLTF act synergistically to suppress G4 accumulation, restrict alternative lengthening of telomeres, and promote resistance to G4-stabilizing drugs. In a discrete but complementary role, HLTF restrains DNA synthesis when G4s are stabilized by suppressing primase-polymerase (PrimPol)-dependent repriming. Together, the distinct roles of HLTF in the G4 response prevent DNA damage and potentially mutagenic replication to safeguard genome stability.