Topoisomerase 1 (TOP1) is an enzyme that regulates DNA topology and is essential for replication, recombination, and other processes. The normal TOP1 catalytic cycle involves the formation of a short-lived covalent complex with the 3′ end of DNA (TOP1 cleavage complex, TOP1cc), which can be stabilized, resulting in cell death. This fact substantiates the effectiveness of anticancer drugs—TOP1 poisons, such as topotecan, that block the relegation of DNA and fix TOP1cc. Tyrosyl-DNA phosphodiesterase 1 (TDP1) is able to eliminate TOP1cc. Thus, TDP1 interferes with the action of topotecan. Poly(ADP-ribose) polymerase 1 (PARP1) is a key regulator of many processes in the cell, such as maintaining the integrity of the genome, regulation of the cell cycle, cell death, and others. PARP1 also controls the repair of TOP1cc. We performed a transcriptomic analysis of wild type and PARP1 knockout HEK293A cells treated with topotecan and TDP1 inhibitor OL9-119 alone and in combination. The largest number of differentially expressed genes (DEGs, about 4000 both up- and down-regulated genes) was found in knockout cells. Topotecan and OL9-119 treatment elicited significantly fewer DEGs in WT cells and negligible DEGs in PARP1-KO cells. A significant part of the changes caused by PARP1-KO affected the synthesis and processing of proteins. Differences under the action of treatment with TOP1 or TDP1 inhibitors alone were found in the signaling pathways for the development of cancer, DNA repair, and the proteasome. The drug combination resulted in DEGs in the ribosome, proteasome, spliceosome, and oxidative phosphorylation pathways.