Low-coverage whole-genome sequencing (also known as "genome skimming") is becoming an increasingly affordable approach to large-scale phylogenetic analyses. While already routinely used to recover organellar genomes, genome skimming is rather rarely utilized for recovering single-copy nuclear markers. One reason might be that only few tools exist to work with this data type within a phylogenomic context, especially to deal with fragmented genome assemblies. We here present a new software tool called Patchwork for mining phylogenetic markers from highly fragmented short-read assemblies as well as directly from sequence reads. Patchwork is an alignment-based tool that utilizes the sequence aligner DIAMOND and is written in the programming language Julia. Homologous regions are obtained via a sequence similarity search, followed by a "hit stitching" phase, in which adjacent or overlapping regions are merged into a single unit. The novel sliding window algorithm trims away any noncoding regions from the resulting sequence. We demonstrate the utility of Patchwork by recovering near-universal single-copy orthologs within a benchmarking study, and we additionally assess the performance of Patchwork in comparison with other programs. We find that Patchwork allows for accurate retrieval of (putatively) single-copy genes from genome skimming data sets at different sequencing depths with high computational speed, outperforming existing software targeting similar tasks. Patchwork is released under the GNU General Public License version 3. Installation instructions, additional documentation, and the source code itself are all available via GitHub at https://github.com/fethalen/Patchwork.