Downregulation of separase, condensin, Smc5/6, topoisomerase II and Cdc14 in Saccharomyces cerevisiae yields anaphase bridges formed by unresolved sister chromatids (SCBs). Here we report that the overlapping actions of the structure-selective endonucleases (SSEs) Mus81-Mms4/EME1 and Yen1/GEN1, but not Slx1-Slx4, are also essential to prevent the formation of spontaneous SCBs that depend on the homologous recombination pathway. We further show that the frequency of SCBs is boosted after mild replication stress and that they contain joint molecules enriched in non-canonical forms of the Holliday junction (HJ), including nicked-HJ (nHJ). We show that SCBs are mostly reversible upon activation of either Mus81-Mms4 or Yen1 in late anaphase, which is concomitant with the disappearance of non-canonical HJs and restoration of viable progeny. On the basis of these findings, we propose a model where unresolved recombination intermediates are a source of mitotic SCBs, and Mus81-Mms4 and Yen1 play a central role in their resolution in vivo.