The development of preferentially selective cancer chemotherapeutics is a new trend in drug research. Thus, we designed and synthesized novel ternary complexes, [Cu(tryp)(Hnor)
2
(DMSO)]NO
3
(
1)
and [Zn(tryp)(Hnor)
2
(DMSO)]NO
3
(2)
(tryp = DL-Tryptophane; Hnor = Norharmane, β-carboline; DMSO = Dimethyl sulfoxide), characterized with elemental analysis, FTIR, UV–vis, FL, NMR, ESI-MS, and molar conductivity. Furthermore, the TD-DFT studies with UV–vis and FTIR validated the proposed structures of
1
and
2
. Moreover, we evaluated the HOMO-LUMO energy gap and found that
1
has a smaller energy gap than
2
. Then,
1
and
2
were assessed for anticancer chemotherapeutic potential against cancer cell lines MCF7 (human breast cancer) and HepG2 (human liver hepatocellular carcinoma) as well as the non-tumorigenic HEK293 (human embryonic kidney) cells. The MTT assay illustrated the preferentially cytotoxic behavior of
1
when compared with that of
2
and cisplatin (standard drug) against MCF7 cells. Moreover,
1
was exposed to MCF7 cells, and the results indicated the arrest of the G2/M phases, which followed the apoptotic pathway predominantly. Generation of ROS, GSH depletion, and elevation in LPO validated the redox changes prompted by
1
. These studies establish the great potential of
1
as a candidate for anticancer therapeutics.