Currently available single-cell omics technologies capture many unique features with different biological information content. Data integration aims to place cells, captured with different technologies, onto a common embedding to facilitate downstream analytical tasks. Current horizontal data integration techniques use a set of common features, thereby ignoring non-overlapping features and losing information. Here we introduce StabMap, a mosaic data integration technique that stabilizes mapping of single-cell data by exploiting the non-overlapping features. StabMap first infers a mosaic data topology based on shared features, then projects all cells onto supervised or unsupervised reference coordinates by traversing shortest paths along the topology. We show that StabMap performs well in various simulation contexts, facilitates 'multi-hop' mosaic data integration where some datasets do not share any features and enables the use of spatial gene expression features for mapping dissociated single-cell data onto a spatial transcriptomic reference.