The use of computational tools has become widespread in drug discovery as an effective approach to guide the development of new therapeutic agents, including potential cancer drugs. In addition, plant-derived secondary metabolites have attracted considerable interest as a valuable source of bioactive compounds. Among these, alkannin and shikonin, two enantiomeric phyto naphthoquinones, have emerged as promising candidates for cancer therapy because of their anti-inflammatory properties and their ability to induce oxidative DNA damage in malignant cells. Related to the above commentaries, in the present study, the phyto naphthoquinones alkannin, shikonin, and their corresponding indole derivatives were evaluated employing density functional theory (DFT), followed by chemoinformatic analyses and molecular docking studies to evaluate, in silico, their potential activity against the cancer-related enzymes PARP-1, COX-2, and HDAC2, which are overexpressed in several types of cancer. The presence of the indole moiety in the phytomolecules increased their chemical reactivity, as exhibited by the calculated properties and the smaller LUMO–HOMO energy gap. In addition, the bioinformatic evaluation predicted that the target molecules may act as potential apoptosis agonists and antineoplastic agents. Finally, the performed molecular docking analysis suggested a stereoselective effect on the stability of ligand–protein binding complexes, particularly for alkannin, including relevant interactions with His201 and its indole derivative displaying interactions with His201, Tyr235, and Glu327 from the PARP-1 catalytic triad. Additionally, alkannin (−11.2 kcal/mol) and the corresponding indole derivative of shikonin (−10.14 kcal/mol) showed better interaction energies with COX-2 than naproxen (−8.75 kcal/mol). In the latter case, the inclusion of the indole moiety improved the binding affinity. In contrast, the affinity of the target compounds for HDAC2 decreased considerably with the indole derivatives in comparison with the reference compound BIZ.