Alternative lengthening of telomeres (ALT) in human cells is a conserved process that is often activated in telomerase-deficient human cancers. This process exploits components of the recombination machinery to extend telomere ends, thus allowing for increased proliferative potential. Human MUS81 (Mus81 in Saccharomyces cerevisiae) is the catalytic subunit of structure-selective endonucleases involved in recombination and has been implicated in the ALT mechanism. However, it is unclear whether MUS81 activity at the telomere is specific to ALT cells or if it is required for more general aspects of telomere stability. In this study, we use S. cerevisiae to evaluate the contribution of the conserved Mus81-Mms4 endonuclease in telomerase-deficient yeast cells that maintain their telomeres by mechanisms akin to human ALT. Similar to human cells, we find that yeast Mus81 readily localizes to telomeres and its activity is important for viability after initial loss of telomerase. Interestingly, our analysis reveals that yeast Mus81 is not required for the survival of cells undergoing recombination-mediated telomere lengthening, i.e. for ALT itself. Rather we infer from genetic analysis that Mus81-Mms4 facilitates telomere replication during times of telomere instability. Furthermore, combining mus81 mutants with mutants of a yeast telomere replication factor, Rrm3, reveals that the two proteins function in parallel to promote normal growth during times of telomere stress. Combined with previous reports, our data can be interpreted in a consistent model in which both yeast and human MUS81-dependent nucleases participate in the recovery of stalled replication forks within telomeric DNA. Furthermore, this process becomes crucial under conditions of additional replication stress, such as telomere replication in telomerase-deficient cells.