The fidelity of epigenetic inheritance or, the precision by which epigenetic information is passed along, is an essential parameter for measuring the effectiveness of the process. How the precision of the process is achieved or modulated, however, remains largely elusive. We have performed quantitative measurement of epigenetic fidelity, using position effect variegation (PEV) in Schizosaccharomyces pombe as readout, to explore whether replication perturbation affects nucleosome-mediated epigenetic inheritance. We show that replication stresses, due to either hydroxyurea treatment or various forms of genetic lesions of the replication machinery, reduce the inheritance accuracy of CENP-A/Cnp1 nucleosome positioning within centromere. Mechanistically, we demonstrate that excessive formation of single-stranded DNA, a common molecular abnormality under these conditions, might have correlation with the reduction in fidelity of centromeric chromatin duplication. Furthermore, we show that replication stress broadly changes chromatin structure at various loci in the genome, such as telomere heterochromatin expanding and mating type locus heterochromatin spreading out of the boundaries. Interestingly, the levels of inheritable expanding at sub-telomeric heterochromatin regions are highly variable among independent cell populations. Finally, we show that HU treatment of the multi-cellular organisms C. elegans and D. melanogaster affects epigenetically programmed development and PEV, illustrating the evolutionary conservation of the phenomenon. Replication stress, in addition to its demonstrated role in genetic instability, promotes variable epigenetic instability throughout the epigenome.