"Active" reservoir cells transcribing HIV can perpetuate chronic inflammation in virally suppressed people with HIV (PWH) and likely contribute to viral rebound after antiretroviral therapy (ART) interruption, so they represent an important target for new therapies. These cells, however, are difficult to study using single-cell RNA-seq (scRNA-seq) due to their low frequency and low levels of HIV transcripts, which are usually not polyadenylated. Here, we developed "HIV-seq" to enable more efficient capture of HIV transcripts - including non-polyadenylated ones - for scRNA-seq analysis of cells from PWH. By spiking in a set of custom-designed capture sequences targeting conserved regions of the HIV genome during scRNA-seq, we increased our ability to find HIV RNA+ cells from PWH by up to 44%. Implementing HIV-seq in conjunction with surface phenotyping by CITE-seq on paired blood specimens from PWH before vs. after ART suppression, we found that HIV RNA+ cells were enriched among T effector memory (Tem) cells during both viremia and ART suppression, but exhibited a cytotoxic signature during viremia only. By contrast, HIV RNA+ cells from the ART-suppressed timepoints exhibited a distinct anti-inflammatory signature involving elevated TGF-β and diminished IFN signaling. Overall, these findings demonstrate that active reservoir cells exhibit transcriptional features distinct from HIV RNA+ cells during viremia, and underscore HIV-seq as a useful tool to better understand the mechanisms by which HIV-transcribing cells can persist during ART.