Tomato yellow leaf curl virus (TYLCV) is a begomovirus infecting tomato plants worldwide. TYLCV needs a healthy host environment to ensure a successful infection cycle for long periods. Hence, TYLCV restrains its destructive effect and induces neither a hypersensitive response nor cell death in infected tomatoes. On the contrary, TYLCV counteracts cell death induced by other factors, such as inactivation of HSP90 functionality. Suppression of plant death is associated with the inhibition of the ubiquitin 26S proteasome degradation and with a deactivation of the heat shock transcription factor HSFA2 pathways (including decreased HSP17 levels). The goal of the current study was to find if the individual TYLCV genes were capable of suppressing HSP90-dependent death and HSFA2 deactivation. The expression of C2 (C3 and CP to a lesser extent) caused a decrease in the severity of death phenotypes, while the expression of V2 (C1 and C4 to a lesser extent) strengthened cell death. However, C2 or V2 markedly affected stress response under conditions of viral infection. The downregulation of HSFA2 signaling, initiated by the expression of C1 and V2, was detected in the absence of virus infection, but was enhanced in infected plants, while CP and C4 mitigated HSFA2 levels only in the infected tomatoes. The dependence of analyzed plant stress response suppression on the interaction of the expressed genes with the environment created by the whole virus infection was more pronounced than on the expression of individual TYLCV genes.