Multidrug resistant (MDR) tuberculosis (TB) is defined by the resistance of Mycobacterium tuberculosis, the causative organism, to the first-line antibiotics rifampicin and isoniazid. Mitigating or reversing resistance to these drugs offers a means of preserving and extending their use in TB treatment. R-loops are RNA/DNA hybrids that are formed in the genome during transcription, and can be lethal to the cell if not resolved. RNase HI is an enzyme that removes R-loops, and this activity is essential in M. tuberculosis: knockouts of rnhC, the gene encoding RNase HI, are non-viable. This essentiality supports it as a candidate target for the development of new antibiotics. In the model organism Mycolicibacterium smegmatis, RNase HI activity is provided by two RNase HI enzymes, RnhA and RnhC. We show that the partial depletion of RNase HI activity in M. smegmatis, by knocking out either of the genes encoding RnhA or RnhC, led to the accumulation of R-loops. The sensitivity of the knockout strains to the antibiotics moxifloxacin, streptomycin and rifampicin was increased, with sensitivity to the transcriptional inhibitor rifampicin strikingly increased by nearly 100-fold. We also show that R-loop accumulation accompanies partial transcriptional inhibition, suggesting a mechanistic basis for the synergy between RNase HI depletion and transcriptional inhibition. A model of how transcriptional inhibition can potentiate R-loop accumulation is presented. Finally, we identified four small molecules that inhibit recombinant RnhC activity and that also potentiated rifampicin activity in whole-cell assays against M. tuberculosis, supporting an on-target mode of action, and providing the first step in developing a new class of anti-mycobacterial drug.