The Bloom syndrome (BLM) helicase is critical for alternative lengthening of telomeres (ALT), a homology-directed repair (HDR)-mediated telomere maintenance mechanism that is prevalent in cancers of mesenchymal origin. The DNA substrates that BLM engages to direct telomere recombination during ALT remain unknown. Here, we determine that BLM helicase acts on lagging strand telomere intermediates that occur specifically in ALT-positive cells to assemble a replication-associated DNA damage response. Loss of ATRX was permissive for BLM localization to ALT telomeres in S and G2, commensurate with the appearance of telomere C-strand-specific single-stranded DNA (ssDNA). DNA2 nuclease deficiency increased 5'-flap formation in a BLM-dependent manner, while telomere C-strand, but not G-strand, nicks promoted ALT. These findings define the seminal events in the ALT DNA damage response, linking aberrant telomeric lagging strand DNA replication with a BLM-directed HDR mechanism that sustains telomere length in a subset of human cancers.