The integrated stress response (ISR) suppresses global translation while allowing selective synthesis of key regulatory proteins. However, how translation persists during ISR remains unclear. In eukaryotes, the 5'-cap of mRNAs is bound by either the cap-binding complex (CBC) or eIF4E. We show that under stress, CBC-bound mRNAs recruit eIF2A, an alternative initiation factor, to sustain translation when eIF4E-dependent translation is inhibited. Human embryonic stem cells (hESCs), which inherently exhibit ISR, continue proliferating due to a compensatory increase in eIF2A. This increase ensures CBC-dependent translation (CT) of essential cell cycle regulators. Notably, yes-associated protein (YAP), a key proliferation factor, is a major CT target driving stress-resistant stem cell proliferation. Our findings reveal CT as a critical pathway that preserves protein synthesis and proliferation under stress.