Programmed cell death (PCD) pathways play a crucial role in the response of cancer cells to treatment. Their dysregulation is one of the cancer hallmarks and one of the reasons of drug resistance. Here, we studied the significance of the individual members of PCD signaling pathways in response to treatment with common anti-cancer drugs using the T-cell leukemia Jurkat cells with single or double knockouts of necroptosis and/or apoptosis genes. We identified apoptosis as the primary cell death pathway upon anti-cancer drugs treatment. The cells with knocked out either Fas-associated protein with death domain (FADD) or all executioner caspases were resistant. This resistance could be partially overcome by induction of RIP1-dependent necroptosis through TNFR1 activation using combined treatment with TNF-alpha and smac mimetic (LCL161). RIP1 was essential for cellular response to TNF-alpha and smac mimetic, but dispensable for the response to anti-cancer drugs. Here, we demonstrated the significance of FADD and executioner caspases in carrying out programmed cell death upon anti-cancer drug treatments and the ability of combined treatment with TNF-alpha and smac mimetic to partially overcome drug resistance of FADD and/or CASP3/7/6-deficient cells via RIP1-dependent necroptosis. Thus, a combination of TNF-alpha and smac mimetic could be a suitable strategy for overcoming resistance to therapy in cells unable to trigger apoptosis.