Intermolecular RNA-RNA interactions are used by many noncoding RNAs (ncRNAs) to achieve their diverse functions. To identify these contacts, we developed a method based on RNA antisense purification to systematically map RNA-RNA interactions (RAP-RNA) and applied it to investigate two ncRNAs implicated in RNA processing: U1 small nuclear RNA, a component of the spliceosome, and Malat1, a large ncRNA that localizes to nuclear speckles. U1 and Malat1 interact with nascent transcripts through distinct targeting mechanisms. Using differential crosslinking, we confirmed that U1 directly hybridizes to 5' splice sites and 5' splice site motifs throughout introns and found that Malat1 interacts with pre-mRNAs indirectly through protein intermediates. Interactions with nascent pre-mRNAs cause U1 and Malat1 to localize proximally to chromatin at active genes, demonstrating that ncRNAs can use RNA-RNA interactions to target specific pre-mRNAs and genomic sites. RAP-RNA is sensitive to lower abundance RNAs as well, making it generally applicable for investigating ncRNAs.