Genome integrity depends on correct chromosome segregation, which in turn relies on cohesion between sister chromatids from S phase until anaphase. S phase cohesion, together with DNA double-strand break (DSB) recruitment of cohesin and formation of damage-induced (DI) cohesion, has previously been shown to be required also for efficient postreplicative DSB repair. The budding yeast acetyltransferase Eco1 (Ctf7) is a common essential factor for S phase and DI-cohesion. The fission yeast Eco1 ortholog, Eso1, is expressed as a fusion protein with the translesion synthesis (TLS) polymerase Polη. The involvement of Eso1 in S phase cohesion was attributed to the Eco1 homologous part of the protein and bypass of UV-induced DNA lesions to the Polη part. Here we describe an additional novel function for budding yeast Polη, i.e. formation of postreplicative DI genome-wide cohesion. This is a unique Polη function not shared with other TLS polymerases. However, Polη deficient cells are DSB repair competent, as Polη is not required for cohesion locally at the DSB. This reveals differential regulation of DSB-proximal cohesion and DI genome-wide cohesion, and challenges the importance of the latter for DSB repair. Intriguingly, we found that specific inactivation of DI genome-wide cohesion increases chromosomal mis-segregation at the entrance of the next cell cycle, suggesting that S phase cohesion is not sufficient for correct chromosome segregation in the presence of DNA damage.