Two novel structural types of tyrosyl-DNA phosphodiesterase 1 (TDP1) inhibitors with hexahydroisobenzofuran 11 and 3-oxabicyclo [3.3.1]nonane 12 scaffolds were discovered. These monoterpene-derived compounds were synthesized through preliminary isomerization of (+)-3-carene to (+)-2-carene followed by reaction with heteroaromatic aldehydes. All the compounds inhibit the TDP1 enzyme at micro- and submicromolar levels, with the most potent compound having an IC50 value of 0.65 μM. TDP1 is an important DNA repair enzyme and a promising target for the development of new chemosensitizing agents. A panel of isogenic clones of the HEK293FT cell line knockout for the TDP1 gene was created using the CRISPR-Cas9 system. Cytotoxic effects of topotecan (Tpc) and non-cytotoxic compounds of the new structures were investigated separately and jointly in the TDP1 gene knockout cells. For two TDP1 inhibitors, 11h and 12k, a synergistic effect was observed with Tpc in the HEK293FT cells but was not found in TDP1 -/- cells. Thus, it is likely that the synergistic effect is caused by inhibition of TDP1. Synergy was also found for 11h in other cancer cell lines. Thus, sensitizing cancer cells using a non-cytotoxic drug can enhance the efficacy of currently used pharmaceuticals and, concomitantly, reduce toxic side effects.