DNA double-strand breaks (DSBs) are potent sources of genome instability. While there is considerable genetic and molecular information about the disposition of direct DSBs and breaks that arise during replication, relatively little is known about DSBs derived during processing of single-strand lesions, especially for the case of single-strand breaks (SSBs) with 3′-blocked termini generated in vivo. Using our recently developed assay for detecting end-processing at random DSBs in budding yeast, we show that single-strand lesions produced by the alkylating agent methyl methanesulfonate (MMS) can generate DSBs in G2-arrested cells, i.e., S-phase independent. These derived DSBs were observed in apn1/2 endonuclease mutants and resulted from aborted base excision repair leading to 3′ blocked single-strand breaks following the creation of abasic (AP) sites. DSB formation was reduced by additional mutations that affect processing of AP sites including ntg1, ntg2, and, unexpectedly, ogg1, or by a lack of AP sites due to deletion of the MAG1 glycosylase gene. Similar to direct DSBs, the derived DSBs were subject to MRX (Mre11, Rad50, Xrs2)-determined resection and relied upon the recombinational repair genes RAD51, RAD52, as well as on the MCD1 cohesin gene, for repair. In addition, we identified a novel DNA intermediate, detected as slow-moving chromosomal DNA (SMD) in pulsed field electrophoresis gels shortly after MMS exposure in apn1/2 cells. The SMD requires nicked AP sites, but is independent of resection/recombination processes, suggesting that it is a novel structure generated during processing of 3′-blocked SSBs. Collectively, this study provides new insights into the potential consequences of alkylation base damage in vivo, including creation of novel structures as well as generation and repair of DSBs in nonreplicating cells.